7.5 Sample test: rational expressions

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

• 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?

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

• 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?

$\frac{{\mathrm{4x}}^3-\mathrm{9x}}{x^2-\mathrm{3x}-\text{10}}\times \frac{{\mathrm{2x}}^2-\text{20}x+\text{50}}{{\mathrm{6x}}^2-\mathrm{9x}}$

• 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?

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

• 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?

$\frac{{\mathrm{6x}}^3-{\mathrm{5x}}^2-\mathrm{5x}+\text{34}}{\mathrm{2x}+3}$

• A

  Solve by long division.

• B

  Check your answer (show your work!!!).

If $f\left(x\right)=x^2$ , find $\frac{f(x+h)-f(x)}{h}$ . Simplify as much as possible.

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

• A

  Solve for $x$ .

• B

  Test one of your answers and show that it works in the original expression. (No credit unless you show your work!)