8.11 Exercise supplement

${\left(x-7\right)}^4÷\frac{{\left(x-7\right)}^3}{x+1}$

${\left(4x+9\right)}^6÷\frac{{\left(4x+9\right)}^2}{{\left(3x+1\right)}^4}$

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

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

$\frac{y^2+4y+4}{y^2+10y+21}÷\left(y+2\right)$

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

$\frac{3x+1}{x^2+3x+2}+\frac{5x+6}{x^2+6x+5}-\frac{3x-7}{x^2-2x-35}$

$\frac{5a+3b}{8a^2+2ab-b^2}-\frac{3a-b}{4a^2-9ab+2b^2}-\frac{a+5b}{4a^2+3ab-b^2}$

$\frac{3x^2+6x+10}{10x^2+11x-6}+\frac{2x^2-4x+15}{2x^2-11x-21}$

$\frac{4x}{5}+\frac{3x-1}{15}=\frac{29}{25}$

$\frac{6a}{7}+\frac{2a-3}{21}=\frac{77}{21}$

$\frac{5x-1}{6}+\frac{3x+4}{9}=\frac{-8}{9}$

$\frac{4y-5}{4}+\frac{8y+1}{6}=\frac{-69}{12}$

$\frac{4}{x-1}+\frac{7}{x+2}=\frac{43}{x^2+x-2}$

$\frac{5}{a+3}+\frac{6}{a-4}=\frac{9}{a^2-a-12}$

$\frac{-5}{y-3}+\frac{2}{y-3}=\frac{3}{y-3}$

$\frac{2m+5}{m-8}+\frac{9}{m-8}=\frac{30}{m-8}$

$\frac{r+6}{r-1}-\frac{3r+2}{r-1}=\frac{-6}{r-1}$

$\frac{8b+1}{b-7}-\frac{b+5}{b-7}=\frac{45}{b-7}$

Solve $z=\frac{x-\overline{x}}{x}\text{\hspace{0.17em}for\hspace{0.17em}}s.$

Solve $A=P\left(1+rt\right)\text{\hspace{0.17em}for\hspace{0.17em}}t.$

Solve $\frac{1}{R}=\frac{1}{E}+\frac{1}{F}\text{\hspace{0.17em}for\hspace{0.17em}}E.$

Solve $Q=\frac{2mn}{s+t}\text{\hspace{0.17em}for\hspace{0.17em}}t.$

Solve $I=\frac{E}{R+r}\text{\hspace{0.17em}for\hspace{0.17em}}r.$

When the same number is subtracted from both terms of the fraction $\frac{7}{12},$ the result is $\frac{1}{2}.$ What is the number?

When the same number is added to both terms of the fraction $\frac{13}{15},$ the result is $\frac{8}{9}.$ What is the number?

When three fourths of a number is added to the reciprocal of the number, the result is $\frac{173}{16}.$ What is the number?

When one third of a number is added to the reciprocal of the number, the result is $\frac{-127}{90}.$ What is the number?

Person A working alone can complete a job in 9 hours. Person B working alone can complete the same job in 7 hours. How long will it take both people to complete the job working together?

Debbie can complete an algebra assignment in $\frac{3}{4}$ of an hour. Sandi, who plays her radio while working, can complete the same assignment in $1\frac{1}{4}$ hours. If Debbie and Sandi work together, how long will it take them to complete the assignment?

An inlet pipe can fill a tank in 6 hours and an outlet pipe can drain the tank in 8 hours. If both pipes are open, how long will it take to fill the tank?

Two pipes can fill a tank in 4 and 5 hours, respectively. How long will it take both pipes to fill the tank?

The pressure due to surface tension in a spherical bubble is given by $P=\frac{4T}{r},$ where $T$ is the surface tension of the liquid, and $r$ is the radius of the bubble.
(a) Determine the pressure due to surface tension within a soap bubble of radius $\frac{1}{2}$ inch and surface tension 22.
(b) Determine the radius of a bubble if the pressure due to surface tension is 57.6 and the surface tension is 18.

The equation $\frac{1}{p}+\frac{1}{q}=\frac{1}{f}$ relates an objects distance $p$ from a lens and the image distance $q$ from the lens to the focal length $f$ of the lens.
(a) Determine the focal length of a lens in which an object 8 feet away produces an image 6 feet away.
(b) Determine how far an object is from a lens if the focal length of the lens is 10 inches and the image distance is 10 inches.
(c) Determine how far an object will be from a lens that has a focal length of $1\frac{7}{8}$ cm and the object distance is 3 cm away from the lens.

$a^2+9a+18$ by $a+3$

$c^2+3c-88$ by $c-8$

$x^3+9x^2+18x+28$ by $x+7$

$y^3-2y^2-49y-6$ by $y+6$

$m^4+2m^3-8m^2-m+2$ by $m-2$

$3r^2-17r-27$ by $r-7$

$a^3-3a^2-56a+10$ by $a-9$

$x^3-x+1$ by $x+3$

$y^3+y^2-y$ by $y+4$

$5x^6+5x^5-2x^4+5x^3-7x^2-8x+6$ by $x^2+x-1$

$y^{10}-y^7+3y^4-3y$ by $y^4-y$

$-4b^7-3b^6-22b^5-19b^4+12b^3-6b^2+b+4$ by $b^2+6$

$x^3+1$ by $x+1$

$a^4+6a^3+4a^2+12a+8$ by $a^2+3a+2$

$y^{10}+6y^5+9$ by $y^5+3$