8.5 Adding and subtracting rational expressions (Page 2/2)

Elementary algebra Page 2 / 2

$\begin{array}{l} \frac{3 x^{2} + 4 x + 5}{(x + 6) (x - 2)} + \frac{2 x^{2} + x + 6}{x^{2} + 4 x - 12} - \frac{x^{2} - 4 x - 6}{x^{2} + 4 x - 12} \\ Factor the denominators to determine if they're the same . \\ \frac{3 x^{2} + 4 x + 5}{(x + 6) (x - 2)} + \frac{2 x^{2} + x + 6}{(x + 6) (x - 2)} - \frac{x^{2} - 4 x - 6}{(x + 6) (x - 2)} \\ The denominators are the same . Combine the numerators being careful to note the negative sign . \\ \frac{3 x^{2} + 4 x + 5 + 2 x^{2} + x + 6 - (x^{2} - 4 x + 6)}{(x + 6) (x - 2)} \\ \frac{3 x^{2} + 4 x + 5 + 2 x^{2} + x + 6 - x^{2} + 4 x + 6}{(x + 6) (x - 2)} \\ \frac{4 x^{2} + 9 x + 17}{(x + 6) (x - 2)} \end{array}$

Got questions? Get instant answers now!

Practice set a

Add or Subtract the following rational expressions.

$\frac{4}{9} + \frac{2}{9}$

$\frac{2}{3}$

Got questions? Get instant answers now!

$\frac{3}{b} + \frac{2}{b}$

$\frac{5}{b}$

Got questions? Get instant answers now!

$\frac{5 x}{2 y^{2}} - \frac{3 x}{2 y^{2}}$

$\frac{x}{y^{2}}$

Got questions? Get instant answers now!

$\frac{x + y}{x - y} + \frac{2 x + 3 y}{x - y}$

$\frac{3 x + 4 y}{x - y}$

Got questions? Get instant answers now!

$\frac{4 x^{2} - x + 4}{3 x + 10} - \frac{x^{2} + 2 x + 5}{3 x + 10}$

$\frac{3 x^{2} - 3 x - 1}{3 x + 10}$

Got questions? Get instant answers now!

$\frac{x (x + 1)}{x (2 x + 3)} + \frac{3 x^{2} - x + 7}{2 x^{2} + 3 x}$

$\frac{4 x^{2} + 7}{x (2 x + 3)}$

Got questions? Get instant answers now!

$\frac{4 x + 3}{x^{2} - x - 6} - \frac{8 x - 4}{(x + 2) (x - 3)}$

$\frac{- 4 x + 7}{(x + 2) (x - 3)}$

Got questions? Get instant answers now!

$\frac{5 a^{2} + a - 4}{2 a (a - 6)} + \frac{2 a^{2} + 3 a + 4}{2 a^{2} - 12 a} + \frac{a^{2} + 2}{2 a^{2} - 12 a}$

$\frac{4 a^{2} + 2 a + 1}{a (a - 6)}$

Got questions? Get instant answers now!

$\frac{8 x^{2} + x - 1}{x^{2} - 6 x + 8} + \frac{2 x^{2} + 3 x}{x^{2} - 6 x + 8} - \frac{5 x^{2} + 3 x - 4}{(x - 4) (x - 2)}$

$\frac{5 x^{2} + x + 3}{(x - 4) (x - 2)}$

Got questions? Get instant answers now!

Fractions with different denominators

Sample set b

Add or Subtract the following rational expressions.

$\begin{array}{l} \frac{4 a}{3 y} + \frac{2 a}{9 y^{2}} . & The denominators are n o t the same . Find the LCD . By inspection, the LCD is 9 y^{2} . \\ \frac{}{9 y^{2}} + \frac{2 a}{9 y^{2}} & \begin{array}{l} The denominator of the first rational expression has been multiplied by 3 y, \\ so the numerator must be multiplied by 3 y . \\ 4 a \cdot 3 y = 12 a y \end{array} \\ \frac{12 a y}{9 y^{2}} + \frac{2 a}{9 y^{2}} & The denominators are now the same . Add the numerators . \\ \frac{12 a y + 2 a}{9 y^{2}} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} \frac{3 b}{b + 2} + \frac{5 b}{b - 3} . & \begin{array}{l} The denominators are n o t the same . The LCD is (b + 2) (b - 3) . \end{array} \\ \frac{}{(b + 2) (b - 3)} + \frac{}{(b + 2) (b - 3)} & \begin{array}{l} The denominator of the first rational expression has been multiplied by b - 3, \\ so the numerator must be multiplied by b - 3. 3 b (b - 3) \end{array} \\ \frac{3 b (b - 3)}{(b + 2) (b - 3)} + \frac{}{(b + 2) (b - 3)} & \begin{array}{l} The denominator of the second rational expression has been multiplied by b + 2, \\ so the numerator must be multiplied by b + 2. 5 b (b + 2) \end{array} \\ \frac{3 b (b - 3)}{(b + 2) (b - 3)} + \frac{5 b (b + 2)}{(b + 2) (b - 3)} & \begin{array}{l} The denominators are now the same . Add the numerators . \end{array} \\ \frac{3 b (b - 3) + 5 b (b + 2)}{(b - 3) (b + 2)} & = & \frac{3 b^{2} - 9 b + 5 b^{2} + 10 b}{(b - 3) (b + 2)} \\ = & \frac{8 b^{2} + b}{(b - 3) (b - 2)} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} \frac{x + 3}{x - 1} + \frac{x - 2}{4 x + 4} . & \begin{array}{l} The denominators are n o t the same . \\ Find the LCD . \end{array} \\ \frac{x + 3}{x - 1} + \frac{x - 2}{4 (x + 1)} & The LCD is (x + 1) (x - 1) \\ \frac{}{4 (x + 1) (x - 1)} + \frac{}{4 (x + 1) (x - 1)} & \begin{array}{l} The denominator of the first rational expression has been multiplied by 4 (x + 1) so \\ the numerator must be multiplied by 4 (x + 1) . 4 (x + 3) (x + 1) \end{array} \\ \frac{4 (x + 3) (x + 1)}{4 (x + 1) (x - 1)} + \frac{}{4 (x + 1) (x - 1)} & \begin{array}{l} The denominator of the second rational expression has been multiplied by x - 1 \\ so the numerator must be multiplied by x - 1. (x - 1) (x - 2) \end{array} \\ \frac{4 (x + 3) (x + 1)}{4 (x + 1) (x - 1)} + \frac{(x - 1) (x - 2)}{4 (x + 1) (x - 1)} & \begin{array}{l} The denominators are now the same. \\ Add the numerators. \end{array} \\ \frac{4 (x + 3) (x + 1) + (x - 1) (x - 2)}{4 (x + 1) (x - 1)} \\ \frac{4 (x^{2} + 4 x + 3) + x^{2} - 3 x + 2}{4 (x + 1) (x - 1)} \\ \frac{4 x^{2} + 16 x + 12 + x^{2} - 3 x + 2}{4 (x + 1) (x - 1)} & = & \frac{5 x^{2} + 13 x + 14}{4 (x + 1) (x - 1)} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} \frac{x + 5}{x^{2} - 7 x + 12} + \frac{3 x - 1}{x^{2} - 2 x - 3} & Determine the LCD . \\ \frac{x + 5}{(x - 4) (x - 3)} + \frac{3 x - 1}{(x - 3) (x + 1)} & The LCD is (x - 4) (x - 3) (x + 1) . \\ \frac{}{(x - 4) (x - 3) (x + 1)} + \frac{}{(x - 4) (x - 3) (x + 1)} & The first numerator must be multiplied by x + 1 and the second by x - 4. \\ \frac{(x + 5) (x + 1)}{(x - 4) (x - 3) (x + 1)} + \frac{(3 x - 1) (x - 4)}{(x - 4) (x - 3) (x + 1)} & The denominators are now the same . Add the numerators . \\ \frac{(x + 5) (x + 1) + (3 x - 1) (x - 4)}{(x - 4) (x - 3) (x + 1)} \\ \frac{x^{2} + 6 x + 5 + 3 x^{2} - 13 x + 4}{(x - 4) (x - 3) (x + 1)} \\ \frac{4 x^{2} - 7 x + 9}{(x - 4) (x - 3) (x + 1)} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} \frac{a + 4}{a^{2} + 5 a + 6} - \frac{a - 4}{a^{2} - 5 a - 24} & Determine the LCD. \\ \frac{a + 4}{(a + 3) (a + 2)} - \frac{a - 4}{(a + 3) (a - 8)} & The LCD is (a + 3) (a + 2) (a - 8) . \\ \frac{}{(a + 3) (a + 2) (a - 8)} - \frac{}{(a + 3) (a + 2) (a - 8)} & The first numerator must be multiplied by a - 8 and the second by a + 2. \\ \frac{(a + 4) (a - 8)}{(a + 3) (a + 2) (a - 8)} - \frac{(a - 4) (a + 2)}{(a + 3) (a + 2) (a - 8)} & The denominators are now the same . Subtract the numerators . \\ \frac{(a + 4) (a - 8) - (a - 4) (a + 2)}{(a + 3) (a + 2) (a - 8)} \\ \frac{a^{2} - 4 a - 32 - (a^{2} - 2 a - 8)}{(a + 3) (a + 2) (a - 8)} \\ \frac{a^{2} - 4 a - 32 - a^{2} + 2 a + 8}{(a + 3) (a + 2) (a - 8)} \\ \frac{- 2 a - 24}{(a + 3) (a + 2) (a - 8)} & Factor - 2 from the numerator . \\ \frac{- 2 (a + 12)}{(a + 3) (a + 2) (a - 8)} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} \frac{3 x}{7 - x} + \frac{5 x}{x - 7} . & \begin{array}{l} The denominators are n e a r l y the same. They differ only in sign. \\ Our technique is to factor - 1 from one of them. \end{array} \\ \frac{3 x}{7 - x} = \frac{3 x}{- (x - 7)} & = & \frac{- 3 x}{x - 7} & Factor - 1 from the first term . \\ \frac{3 x}{7 - x} + \frac{5 x}{x - 7} & = & \frac{- 3 x}{x - 7} + \frac{5 x}{x - 7} \\ = & \frac{- 3 x + 5 x}{x - 7} \\ = & \frac{2 x}{x - 7} \end{array}$

Got questions? Get instant answers now!

Practice set b

Add or Subtract the following rational expressions.

$\frac{3 x}{4 a^{2}} + \frac{5 x}{12 a^{3}}$

$\frac{9 a x + 5 x}{12 a^{3}}$

Got questions? Get instant answers now!

$\frac{5 b}{b + 1} + \frac{3 b}{b - 2}$

$\frac{8 b^{2} - 7 b}{(b + 1) (b - 2)}$

Got questions? Get instant answers now!

$\frac{a - 7}{a + 2} + \frac{a - 2}{a + 3}$

$\frac{2 a^{2} - 4 a - 25}{(a + 2) (a + 3)}$

Got questions? Get instant answers now!

$\frac{4 x + 1}{x + 3} - \frac{x + 5}{x - 3}$

$\frac{3 x^{2} - 19 x - 18}{(x + 3) (x - 3)}$

Got questions? Get instant answers now!

$\frac{2 y - 3}{y} + \frac{3 y + 1}{y + 4}$

$\frac{5 y^{2} + 6 y - 12}{y (y + 4)}$

Got questions? Get instant answers now!

$\frac{a - 7}{a^{2} - 3 a + 2} + \frac{a + 2}{a^{2} - 6 a + 8}$

$\frac{2 a^{2} - 10 a + 26}{(a - 2) (a - 1) (a - 4)}$

Got questions? Get instant answers now!

$\frac{6}{b^{2} + 6 b + 9} - \frac{2}{b^{2} + 4 b + 4}$

$\frac{4 b^{2} + 12 b + 6}{{(b + 3)}^{2} {(b + 2)}^{2}}$

Got questions? Get instant answers now!

$\frac{x}{x + 4} - \frac{x - 2}{3 x - 3}$

$\frac{2 x^{2} - 5 x + 8}{3 (x + 4) (x - 1)}$

Got questions? Get instant answers now!

$\frac{5 x}{4 - x} + \frac{7 x}{x - 4}$

$\frac{2 x}{x - 4}$

Got questions? Get instant answers now!

Sample set c

Combine the following rational expressions.

$\begin{array}{l} 3 + \frac{7}{x - 1} . & Rewrite the expression. \\ \frac{3}{1} + \frac{7}{x - 1} & The LCD is x - 1. \\ \frac{3 (x - 1)}{x - 1} + \frac{7}{x - 1} & = & \frac{3 x - 3}{x - 1} + \frac{7}{x - 1} & = & \frac{3 x - 3 + 7}{x - 1} \\ = & \frac{3 x + 4}{x - 1} \end{array}$

Got questions? Get instant answers now!

$\begin{array}{l} 3 y + 4 - \frac{y^{2} - y + 3}{y - 6} . & Rewrite the expression. \\ \frac{3 y + 4}{1} - \frac{y^{2} - y + 3}{y - 6} & The LCD is y - 6. \\ \frac{(3 y + 4) (y - 6)}{y - 6} - \frac{y^{2} - y + 3}{y - 6} & = & \frac{(3 y + 4) (y - 6) - (y^{2} - y + 3)}{y - 6} \\ = & \frac{3 y^{2} - 14 y - 24 - y^{2} + y - 3}{y - 6} \\ = & \frac{2 y^{2} - 13 y - 27}{y - 6} \end{array}$

Got questions? Get instant answers now!

Practice set c

Simplify $8 + \frac{3}{x - 6} .$

$\frac{8 x - 45}{x - 6}$

Got questions? Get instant answers now!

Simplify $2 a - 5 - \frac{a^{2} + 2 a - 1}{a + 3} .$

$\frac{a^{2} - a - 14}{a + 3}$

Got questions? Get instant answers now!

Exercises

For the following problems, add or subtract the rational expressions.

$\frac{3}{8} + \frac{1}{8}$

$\frac{1}{2}$

Got questions? Get instant answers now!

$\frac{1}{9} + \frac{4}{9}$

Got questions? Get instant answers now!

$\frac{7}{10} - \frac{2}{5}$

$\frac{3}{10}$

Got questions? Get instant answers now!

$\frac{3}{4} - \frac{5}{12}$

Got questions? Get instant answers now!

$\frac{3}{4 x} + \frac{5}{4 x}$

$\frac{2}{x}$

Got questions? Get instant answers now!

$\frac{2}{7 y} + \frac{3}{7 y}$

Got questions? Get instant answers now!

$\frac{6 y}{5 x} + \frac{8 y}{5 x}$

$\frac{14 y}{5 x}$

Got questions? Get instant answers now!

$\frac{9 a}{7 b} + \frac{3 a}{7 b}$

Got questions? Get instant answers now!

$\frac{15 n}{2 m} - \frac{6 n}{2 m}$

$\frac{9 n}{2 m}$

Got questions? Get instant answers now!

$\frac{8 p}{11 q} - \frac{3 p}{11 q}$

Got questions? Get instant answers now!

$\frac{y + 4}{y - 6} + \frac{y + 8}{y - 6}$

$\frac{2 y + 12}{y - 6}$

Got questions? Get instant answers now!

$\frac{y - 1}{y + 4} + \frac{y + 7}{y + 4}$

Got questions? Get instant answers now!

$\frac{a + 6}{a - 1} + \frac{3 a + 5}{a - 1}$

$\frac{4 a + 11}{a - 1}$

Got questions? Get instant answers now!

$\frac{5 a + 1}{a + 7} + \frac{2 a - 6}{a + 7}$

Got questions? Get instant answers now!

$\frac{x + 1}{5 x} + \frac{x + 3}{5 x}$

$\frac{2 x + 4}{5 x}$

Got questions? Get instant answers now!

$\frac{a - 6}{a + 2} + \frac{a - 2}{a + 2}$

Got questions? Get instant answers now!

$\frac{b + 1}{b - 3} + \frac{b + 2}{b - 3}$

$\frac{2 b + 3}{b - 3}$

Got questions? Get instant answers now!

$\frac{a + 2}{a - 5} - \frac{a + 3}{a - 5}$

Got questions? Get instant answers now!

$\frac{b + 7}{b - 6} - \frac{b - 1}{b - 6}$

$\frac{8}{b - 6}$

Got questions? Get instant answers now!

$\frac{2 b + 3}{b + 1} - \frac{b - 4}{b + 1}$

Got questions? Get instant answers now!

$\frac{3 y + 4}{y + 8} - \frac{2 y - 5}{y + 8}$

$\frac{y + 9}{y + 8}$

Got questions? Get instant answers now!

$\frac{2 a - 7}{a - 9} + \frac{3 a + 5}{a - 9}$

Got questions? Get instant answers now!

$\frac{8 x - 1}{x + 2} - \frac{15 x + 7}{x + 2}$

$\frac{- 7 x - 8}{x + 2}$

Got questions? Get instant answers now!

$\frac{7}{2 x^{2}} + \frac{1}{6 x^{3}}$

Got questions? Get instant answers now!

$\frac{2}{3 x} + \frac{4}{6 x^{2}}$

$\frac{2 (x + 1)}{3 x^{2}}$

Got questions? Get instant answers now!

$\frac{5}{6 y^{3}} - \frac{2}{18 y^{5}}$

Got questions? Get instant answers now!

$\frac{2}{5 a^{2}} - \frac{1}{10 a^{3}}$

$\frac{4 a - 1}{10 a^{3}}$

Got questions? Get instant answers now!

$\frac{3}{x + 1} + \frac{5}{x - 2}$

Got questions? Get instant answers now!

$\frac{4}{x - 6} + \frac{1}{x - 1}$

$\frac{5 (x - 2)}{(x - 6) (x - 1)}$

Got questions? Get instant answers now!

$\frac{2 a}{a + 1} - \frac{3 a}{a + 4}$

Got questions? Get instant answers now!

$\frac{6 y}{y + 4} + \frac{2 y}{y + 3}$

$\frac{2 y (4 y + 13)}{(y + 4) (y + 3)}$

Got questions? Get instant answers now!

$\frac{x - 1}{x - 3} + \frac{x + 4}{x - 4}$

Got questions? Get instant answers now!

$\frac{x + 2}{x - 5} + \frac{x - 1}{x + 2}$

$\frac{2 x^{2} - 2 x + 9}{(x - 5) (x + 2)}$

Got questions? Get instant answers now!

$\frac{a + 3}{a - 3} - \frac{a + 2}{a - 2}$

Got questions? Get instant answers now!

$\frac{y + 1}{y - 1} - \frac{y + 4}{y - 4}$

$\frac{- 6 y}{(y - 1) (y - 4)}$

Got questions? Get instant answers now!

$\frac{x - 1}{(x + 2) (x - 3)} + \frac{x + 4}{x - 3}$

Got questions? Get instant answers now!

$\frac{y + 2}{(y + 1) (y + 6)} + \frac{y - 2}{y + 6}$

$\frac{y^{2}}{(y + 1) (y + 6)}$

Got questions? Get instant answers now!

$\frac{2 a + 1}{(a + 3) (a - 3)} - \frac{a + 2}{a + 3}$

Got questions? Get instant answers now!

$\frac{3 a + 5}{(a + 4) (a - 1)} - \frac{2 a - 1}{a - 1}$

$\frac{- 2 a^{2} - 4 a + 9}{(a + 4) (a - 1)}$

Got questions? Get instant answers now!

$\frac{2 x}{x^{2} - 3 x + 2} + \frac{3}{x - 2}$

Got questions? Get instant answers now!

$\frac{4 a}{a^{2} - 2 a - 3} + \frac{3}{a + 1}$

$\frac{7 a - 9}{(a + 1) (a - 3)}$

Got questions? Get instant answers now!

$\frac{3 y}{y^{2} - 7 y + 12} - \frac{y^{2}}{y - 3}$

Got questions? Get instant answers now!

$\frac{x - 1}{x^{2} + 6 x + 8} + \frac{x + 3}{x^{2} + 2 x - 8}$

$\frac{2 (x^{2} + x + 4)}{(x + 2) (x - 2) (x + 4)}$

Got questions? Get instant answers now!

$\frac{a - 4}{a^{2} + 2 a - 3} + \frac{a + 2}{a^{2} + 3 a - 4}$

Got questions? Get instant answers now!

$\frac{b - 3}{b^{2} + 9 b + 20} + \frac{b + 4}{b^{2} + b - 12}$

$\frac{2 b^{2} + 3 b + 29}{(b - 3) (b + 4) (b + 5)}$

Got questions? Get instant answers now!

$\frac{y - 1}{y^{2} + 4 y - 12} - \frac{y + 3}{y^{2} + 6 y - 16}$

Got questions? Get instant answers now!

$\frac{x + 3}{x^{2} + 9 x + 14} - \frac{x - 5}{x^{2} - 4}$

$\frac{- x + 29}{(x - 2) (x + 2) (x + 7)}$

Got questions? Get instant answers now!

$\frac{x - 1}{x^{2} - 4 x + 3} + \frac{x + 3}{x^{2} - 5 x + 6} + \frac{2 x}{x^{2} - 3 x + 2}$

Got questions? Get instant answers now!

$\frac{4 x}{x^{2} + 6 x + 8} + \frac{3}{x^{2} + x - 6} + \frac{x - 1}{x^{2} + x - 12}$

$\frac{5 x^{4} - 3 x^{3} - 34 x^{2} + 34 x - 60}{(x - 2) (x + 2) (x - 3) (x + 3) (x + 4)}$

Got questions? Get instant answers now!

$\frac{y + 2}{y^{2} - 1} + \frac{y - 3}{y^{2} - 3 y - 4} - \frac{y + 3}{y^{2} - 5 y + 4}$

Got questions? Get instant answers now!

$\frac{a - 2}{a^{2} - 9 a + 18} + \frac{a - 2}{a^{2} - 4 a - 12} - \frac{a - 2}{a^{2} - a - 6}$

$\frac{(a + 5) (a - 2)}{(a + 2) (a - 3) (a - 6)}$

Got questions? Get instant answers now!

$\frac{y - 2}{y^{2} + 6 y} + \frac{y + 4}{y^{2} + 5 y - 6}$

Got questions? Get instant answers now!

$\frac{a + 1}{a^{3} + 3 a^{2}} - \frac{a + 6}{a^{2} - a}$

$\frac{- a^{3} - 8 a^{2} - 18 a - 1}{a^{2} (a + 3) (a - 1)}$

Got questions? Get instant answers now!

$\frac{4}{3 b^{2} - 12 b} - \frac{2}{6 b^{2} - 6 b}$

Got questions? Get instant answers now!

$\frac{3}{2 x^{5} - 4 x^{4}} + \frac{- 2}{8 x^{3} + 24 x^{2}}$

$\frac{- x^{3} + 2 x^{2} + 6 x + 18}{4 x^{4} (x - 2) (x + 3)}$

Got questions? Get instant answers now!

$\frac{x + 2}{12 x^{3}} + \frac{x + 1}{4 x^{2} + 8 x - 12} - \frac{x + 3}{16 x^{2} - 32 x + 16}$

Got questions? Get instant answers now!

$\frac{2 x}{x^{2} - 9} - \frac{x + 1}{4 x^{2} - 12 x} - \frac{x - 4}{8 x^{3}}$

$\frac{14 x^{4} - 9 x^{3} - 2 x^{2} + 9 x - 36}{8 x^{3} (x + 3) (x - 3)}$

Got questions? Get instant answers now!

$4 + \frac{3}{x + 2}$

Got questions? Get instant answers now!

$8 + \frac{2}{x + 6}$

$\frac{8 x + 50}{x + 6}$

Got questions? Get instant answers now!

$1 + \frac{4}{x - 7}$

Got questions? Get instant answers now!

$3 + \frac{5}{x - 6}$

$\frac{3 x - 13}{x - 6}$

Got questions? Get instant answers now!

$- 2 + \frac{4 x}{x + 5}$

Got questions? Get instant answers now!

$- 1 + \frac{3 a}{a - 1}$

$\frac{2 a + 1}{a - 1}$

Got questions? Get instant answers now!

$6 - \frac{4 y}{y + 2}$

Got questions? Get instant answers now!

$2 x + \frac{x^{2} - 4}{x + 1}$

$\frac{3 x^{2} + 2 x - 4}{x + 1}$

Got questions? Get instant answers now!

$- 3 y + \frac{4 y^{2} + 2 y - 5}{y + 3}$

Got questions? Get instant answers now!

$x + 2 + \frac{x^{2} + 4}{x - 1}$

$\frac{2 x^{2} + x + 2}{x - 1}$

Got questions? Get instant answers now!

$b + 6 + \frac{2 b + 5}{b - 2}$

Got questions? Get instant answers now!

$\frac{3 x - 1}{x - 4} - 8$

$\frac{- 5 x + 31}{x - 4}$

Got questions? Get instant answers now!

$\frac{4 y + 5}{y + 1} - 9$

Got questions? Get instant answers now!

$\frac{2 y^{2} + 11 y - 1}{y + 4} - 3 y$

$\frac{- (y^{2} + y + 1)}{y + 4}$

Got questions? Get instant answers now!

$\frac{5 y^{2} - 2 y + 1}{y^{2} + y - 6} - 2$

Got questions? Get instant answers now!

$\frac{4 a^{3} + 2 a^{2} + a - 1}{a^{2} + 11 a + 28} + 3 a$

$\frac{7 a^{3} + 35 a^{2} + 85 a - 1}{(a + 7) (a + 4)}$

Got questions? Get instant answers now!

$\frac{2 x}{1 - x} + \frac{6 x}{x - 1}$

Got questions? Get instant answers now!

$\frac{5 m}{6 - m} + \frac{3 m}{m - 6}$

$\frac{- 2 m}{m - 6}$

Got questions? Get instant answers now!

$\frac{- a + 7}{8 - 3 a} + \frac{2 a + 1}{3 a - 8}$

Got questions? Get instant answers now!

$\frac{- 2 y + 4}{4 - 5 y} - \frac{9}{5 y - 4}$

$\frac{2 y - 13}{5 y - 4}$

Got questions? Get instant answers now!

$\frac{m - 1}{1 - m} - \frac{2}{m - 1}$

Got questions? Get instant answers now!

Exercises for review

( [link] ) Simplify ${(x^{3} y^{2} z^{5})}^{6} {(x^{2} y z)}^{2} .$

$x^{22} y^{14} z^{32}$

Got questions? Get instant answers now!

( [link] ) Write $6 a^{- 3} b^{4} c^{- 2} a^{- 1} b^{- 5} c^{3}$ so that only positive exponents appear.

Got questions? Get instant answers now!

( [link] ) Construct the graph of $y = - 2 x + 4.$
An xy coordinate plane with gridlines, labeled negative five to five on both axes.

A graph of a line passing through three points with coordinates zero, four; one, two; and two, zero.

Got questions? Get instant answers now!

( [link] ) Find the product: $\frac{x^{2} - 3 x - 4}{x^{2} + 6 x + 5} \cdot \frac{x^{2} + 5 x + 6}{x^{2} - 2 x - 8} .$

Got questions? Get instant answers now!

( [link] ) Replace N with the proper quantity: $\frac{x + 3}{x - 5} = \frac{N}{x^{2} - 7 x + 10} .$

$(x + 3) (x - 2)$

Got questions? Get instant answers now!

Questions & Answers

how to create a software using Android phone

Wiseman Reply

how

basra

what is the difference between C and C++.

Yan Reply

what is software

Sami Reply

software is a instructions like programs

Shambhu

what is the difference between C and C++.

Yan

yes, how?

Hayder

what is software engineering

Ahmad

software engineering is a the branch of computer science deals with the design,development, testing and maintenance of software applications.

Hayder

who is best bw software engineering and cyber security

Ahmad

Both software engineering and cybersecurity offer exciting career prospects, but your choice ultimately depends on your interests and skills. If you enjoy problem-solving, programming, and designing software syste

Hayder

what's software processes

Ntege Reply

I haven't started reading yet. by device (hardware) or for improving design Lol? Here. Requirement, Design, Implementation, Verification, Maintenance.

Vernon

I can give you a more valid answer by 5:00 By the way gm.

Vernon

it is all about designing,developing, testing, implementing and maintaining of software systems.

Ehenew

hello assalamualaikum

Sami

My name M Sami I m 2nd year student

Sami

what is the specific IDE for flutter programs?

Mwami Reply

jegudgdtgd my Name my Name is M and I have been talking about iey my papa john's university of washington post I tagged I will be in

Mwaqas Reply

yes

usman

how disign photo

atul Reply

hlo

Navya

Michael

yes

Subhan

Show the necessary steps with description in resource monitoring process (CPU,memory,disk and network)

samuel Reply

What is software engineering

Tafadzwa Reply

Software engineering is a branch of computer science directed to writing programs to develop Softwares that can drive or enable the functionality of some hardwares like phone , automobile and others

kelvin

if any requirement engineer is gathering requirements from client and after getting he/she Analyze them this process is called

Alqa Reply

The following text is encoded in base 64. Ik5ldmVyIHRydXN0IGEgY29tcHV0ZXIgeW91IGNhbid0IHRocm93IG91dCBhIHdpbmRvdyIgLSBTdGV2ZSBXb3puaWFr Decode it, and paste the decoded text here

Julian Reply

what to do you mean

Vincent

hello

ALI

how are you ?

ALI

What is the command to list the contents of a directory in Unix and Unix-like operating systems

George Reply

how can i make my own software free of cost

Faizan Reply

like how

usman

Hayder

The name of the author of our software engineering book is Ian Sommerville.

Doha Reply

what is software

Sampson Reply

the set of intruction given to the computer to perform a task

Noor

Got questions? Join the online conversation and get instant answers!

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask

	7 Sample set b By OpenStax Read Online Course
	5 Practice set a By OpenStax Read Online Course
	25 AP 25 Urinary System Essay By OpenStax Start Flashcards
	4 Practice Neuroanatomy MCQ Exam By David Corey Start Exam
	1 Endocrinology (MCQ) By Rohini Ajay Start Quiz
©flickr: BK	Self Confidence By Miranda Reising Start Quiz
	Introductory statistics By OpenStax Read Online Course
	NCE Ch 06 Groups By Anh Dao Start Quiz
	Art History ARTH209 20th Century By Rebecca Butterfield Start Quiz
	11 AP 11 Muscular System Essay By OpenStax Start Flashcards
	11 Neuroanatomy 11 The Cerebellum By Stephen Voron Start Quiz
	5 Microbiology Final Practice By Madison Christian Start Assignment