Rational Expressions

When adding rational expressions, you must add numerators together and denominators together.

• True

• False

Tags

CCSS.HSA.APR.D.7

Given the sum

 $\frac{3x}{x+2}+\frac{6x+1}{\left(x+2\right)\left(x-5\right)}$  


What is the LCD (lowest common denominator)?

•  $\left(x+2\right)\left(x+2\right)\left(x-5\right)$  

•  $\left(x+2\right)\left(x-5\right)$  

•  $x-5$  

•  $x+2$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Given

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

What values will make the rational expression UNDEFINED?

•  $x=-1,\ x=7$  

•  $x=-1,\ x=4,\ x=7,\ x=-3$  

• None

•  $x=4\ ,\ x=-3$  

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

•  $1$  

•  $\frac{x-1}{x+7}$  

•  $\frac{1}{x+7}$  

•  $\frac{2x^2-5x-12}{x+7}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

Simplify $\frac{x^2+x-30}{2x-10}$   

•  $x+3$  

•  $\frac{x^2-3}{2}$  

•  $\frac{x+6}{2x-2}$  

•  $\frac{x+6}{2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\frac{x^2+10x+25}{x^2-9}\cdot\frac{x^2+3x}{x+5}=$  

•  $\frac{x\left(x+5\right)}{x+3}$  

•  $\frac{x\left(x-5\right)}{x-3}$  

•  $\frac{x\left(x+5\right)}{x-3}$  

•  $\frac{x\left(x-5\right)}{x+3}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

 $\frac{30}{x^2+4x-12}\div\frac{6x}{x-2}=$  

•  $\frac{5}{x\left(x+6\right)}$  

•  $\frac{5}{x\left(x-6\right)}$  

•  $\frac{180x}{\left(x+6\right)\left(x-2\right)}$  

•  $\frac{5}{x+6}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

 $\frac{2m-n}{8n}+\frac{6m-3n}{8n}=$  

•  $m-1$  

•  $\frac{8m-4n}{16m^2}$  

•  $\frac{2m-n}{2n}$  

•  $\frac{8m+2n}{8n}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\frac{x^2-y^2}{2x-2y}\div\frac{8}{x+y}=$  

•  $\frac{1}{16}$  

•  $\frac{\left(x+y\right)^2}{16}$  

•  $\frac{x+y}{8}$  

•  $\frac{\left(x+y\right)\left(x-y\right)}{16}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

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

•  $\frac{x-6}{x+9}$  

•  $\frac{x+6}{x+9}$  

•  $\frac{x+6}{x-9}$  

•  $\frac{x-6}{x-9}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3