Operations with Rational Expressions

Write the rational expression in simplest form:
  $\frac{x^2+6x-27}{x^2-9}$  

•  $\frac{x-9}{x-3}$  

•  $\frac{x+9}{x+3}$  

•  $\frac{x^2+6x-27}{x^2-9}$  

•  $\frac{x-3}{x-3}$  

Write the rational expression in simplest form:

 $\frac{x^4+9x^3}{9x^2}$  

•  $x+9$  

•  $\frac{x\left(x+9\right)}{9}$  

•  $\frac{x+9}{9}$  

•  $\frac{x^4+9x^3}{9x^2}$  

What are the restrictions of:    $\frac{8x}{\left(x+4\right)\left(x-5\right)}$  

(Pick all that apply!)

•  $x\ne5$  

•  $x\ne-5$  

•  $x\ne0$  

•  $x\ne4$  

•  $x\ne-4$  

Write the following sum in simplest form:

 $\frac{9x}{21}+\frac{x+7}{7}$  

•  $12x$  

•  $\frac{12x+7}{21}$  

•  $\frac{12x+21}{21}$  

•  $\frac{84x+147}{147}$  

Tags

CCSS.HSA.APR.D.7

Write the following quotient in simplest form:

 $\frac{8\left(p-1\right)}{p+3}\div\frac{p-1}{p+3}$  

•  $8$  

•  $\frac{8p-1}{p+3}$  

•  $\frac{8\left(p-1\right)\left(p+3\right)}{\left(p+3\right)\left(p-1\right)}$  

•  $\frac{8\left(p-1\right)\left(p+3\right)\ +\ \left(p-1\right)\left(p+3\right)}{\left(p+3\right)\left(p-1\right)}$  

Tags

CCSS.HSA.APR.D.6

Write the following difference in simplest form:

 $\frac{-4x-5}{8}-\frac{-2x+4}{8}$  

•  $\frac{-2x-1}{8}$  

•  $\frac{-2x-9}{16}$  

•  $\frac{-2x-9}{8}$  

•  $\frac{-2x-1}{16}$  

Write this product in simplest form:

 $\frac{h^2+3h}{2}\cdot\frac{4}{h+3}$  

•  $\frac{4\left(h^2+3h\right)}{2\left(h+3\right)}$  

•  $\frac{2h^2+3h}{h+3}$  

•  $2h$  

•  $\frac{2\left(h^2+3h\right)}{h+3}$  

Tags

CCSS.HSA.APR.D.7

Divide and select the answer in simplest form:

 $\frac{x+3}{7x-63}\div\frac{x^2+2x-3}{x^2-10x+9}$  

•  $\frac{\left(x+3\right)}{7\left(x+3\right)}$  

•  $\frac{\left(x+3\right)\left(x-1\right)\left(x+3\right)}{7\left(x-9\right)\left(x-1\right)\left(x-9\right)}$  

•  $7$  

•  $\frac{1}{7}$  

 Write the following sum in simplest form:

 $\frac{4}{m+1}+\frac{8}{m}$ 

•  $\frac{12m+8}{m\left(m+1\right)}$  

•  $\frac{13}{m+1}$  

•  $\frac{12m+1}{m^2+1}$  

•  $\frac{12m+1}{m\left(m+1\right)}$  

Tags

CCSS.HSA.APR.D.7

Write the following quotient in simplest form:

 $\frac{7x+1}{x-7}-\frac{5}{x^2-15x+56}$  

•  $\frac{7x-4}{\left(x-7\right)\left(x-8\right)}$  

•  $\frac{7x^2-55x-8}{\left(x-8\right)\left(x-7\right)}$  

•  $\frac{7x^2-55x-13}{\left(x-8\right)\left(x-7\right)}$  

•  $\frac{7x+6}{x-7}$