Integrated Algebra Quiz: Simplifying Rational Expressions

Which polynomial represents the difference of perfect squares?

•  $x^2-8$  

•  $x^2+16$  

•  $4x^2-49$  

•  $x^2-3$  

•  $4x^2-27$  

 $Simplify\ Completely:\ \ \frac{40x^4+15x^3}{80x^5}$  

Leave the answer in fully factored form.

•  $\frac{8x+3}{16x^2}$  

•  $2x+6x^2$  

•  $\frac{65x^7}{80x^5}$  

•  $\frac{16x^7}{8x^2}$  

•  $\frac{x+3}{2x^2}$  

 $Simplify\ Completely:\ \ \frac{x^2+13x+36}{x^2+4x}$  

Leave the answer in fully factored form.

•  $\frac{10}{x}$  

•  $\frac{x-9}{x}$  

•  $\frac{x+9}{x}$  

•  $\frac{x+9}{x^2}$  

 $Simplify\ Completely:\ \ \ \frac{x^2-4x-45}{x^2-81}$  

Leave the answer in fully factored form.

•  $\frac{x+5}{x-9}$  

•  $\frac{x+5}{x+9}$  

•  $\frac{x-5}{x-9}$  

•  $\frac{x-5}{x+9}$  

What are the steps for Simplifying Rational Expressions?

• Factor Numerator

  Factor Denominator

  Divide Out Like Terms

• Factor Denominator

  Divide Out Like Terms

  Factor Numerator

• Factor Numerator

  Divide Out Like Terms

  Denominator is Already Factored

• Factor Numerator

  Divide Out Like Terms

  Factor Denominator

Tags

CCSS.HSA.APR.D.6

Simplify the expression completely $\ \ \frac{x^2-2x-24}{x^2-5x-36}$  

Leave the answer in fully factored form. 

•  $\frac{x-6}{x+9}$  

•  $\frac{x+6}{x+9}$  

•  $\frac{x+6}{x-9}$  

•  $\frac{x-6}{x-9}$  

 $Simplify\ Completely:\ \ \frac{72}{16x-32}$ 

Leave the answer in fully factored form.

•  $\frac{9}{2x-32}$  

•  $\frac{9}{2x-4}$  

•  $\frac{9}{2\left(x-2\right)}$  

•  $\frac{36}{8x-16}$  

Which factor cancels when you simplify : 

 $\ \ \ \frac{4g^2+3g-10}{2g^2-8}$ 

•  $g-2$  

•  $g+2$  

•  $4g-5$  

•  $2$  

•  $g^2$  

What is the result of simplifying the expression completely. $\ \ \ \frac{2x^2+24x-90}{3x^2-27x+54}$   
Express the answer in fully factored form.

•  $\frac{x+15}{x-6}$  

•  $\frac{2x+30}{3x-18}$  

•  $\frac{2\left(x-15\right)}{3\left(x+6\right)}$  

•  $\frac{2\left(x+15\right)}{3\left(x-6\right)}$  

What is the result of simplifying the expression completely. $\ \ \ \frac{2n^2-3n-20}{3n^2-10n-8}$   
Leave the answer in fully factored form.

•  $\frac{2n+5}{3n+2}$  

•  $\frac{2n-5}{3n-2}$  

•  $\frac{2n-5}{3n+2}$  

•  $\frac{2n+5}{3n-2}$