7.1 Homework: rational expressions

$\frac{x^2-\mathrm{6x}+5}{x^2-\text{16}}\times \frac{x^2+\mathrm{8x}+\text{16}}{x^2-\mathrm{7x}+\text{10}}$

• A

  Simplify

• B

  What values of $x$ are not allowed in the original expression?

• C

  What values of $x$ are not allowed in your simplified expression?

$\frac{\frac{2x^2+7x+3}{x^3+4x}}{\frac{x^2+x-6}{3x}}$

• A

  Simplify

• B

  What values of $x$ are not allowed in the original expression?

• C

  What values of $x$ are not allowed in your simplified expression?

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

• A

  Simplify

• B

  What values of $x$ are not allowed in the original expression?

• C

  What values of $x$ are not allowed in your simplified expression?

• D

  Test your answer by choosing an $x$ value and plugging it into the original expression, and your simplified expression. Do they yield the same answer?

$\frac{x-3}{x^2+\mathrm{9x}+\text{20}}-\frac{x-4}{x^2+\mathrm{8x}+\text{15}}$

• A

  Simplify

• B

  What values of $x$ are not allowed in the original expression?

• C

  What values of $x$ are not allowed in your simplified expression?

$\frac{x+1}{{\mathrm{4x}}^2-9}+\frac{\mathrm{4x}}{{\mathrm{6x}}^2-\mathrm{9x}}$

• A

  Simplify.

• B

  Test your answer by choosing an $x$ value and plugging it into the original expression, and your simplified expression. Do they yield the same answer?