Operations with Rational Expressions

1) $\frac{n^2+8x+15}{n^2-25}$  

•  $\frac{3}{-5}$  

•  $\frac{n+3}{n-5}$  

•  $\frac{8n+15}{-25}$  

•  $\frac{n+3}{n+5}$  

Tags

CCSS.HSA.APR.D.6

What are the domain restrictions for Problem 1?

• $n\ne\pm5$

• $n\ne5$

• $n\ne\pm5,\ -3$

• $n\ne-3,\ 5$

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.CED.A.3

2) $\frac{3a^3-15a^2-4a+20}{2a^3-250}$  

•  $\frac{3a^2-4}{2\left(a^2+5a+25\right)}$  

•  $\frac{3a^2-4}{2\left(a+5\right)^2}$  

•  $\frac{3a^2-2}{a^2+5a+25}$  

•  $\frac{3a^2-4a+2}{5}$  

Tags

CCSS.HSA.APR.D.6

What are the domain restrictions for Problem 2?

•  $a\ne\pm5$ 

•  $a\ne5$ 

•  $a\ne0$ 

•  $a\ne0,\ 5$ 

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.CED.A.3

3) $\frac{2x-3}{\left(x+3\right)^2}\cdot\frac{x^2+4x+3}{9-4x^2}$  

•  $\frac{x+1}{\left(x+3\right)\left(2x+3\right)}$  

•  $-\frac{x+1}{\left(2x+3\right)}$  

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

•  $\frac{1}{\left(2x+3\right)}$  

Tags

CCSS.HSA.APR.D.6

What are the domain restrictions for Problem 3?

•  $x\ne-3,\ -\frac{3}{2}$ 

•  $x\ne-3,\ -\frac{2}{3}$ 

•  $x\ne-3,\ \pm\frac{3}{2}$ 

•  $x\ne0,\ -1,\ -3$ 

Tags

CCSS.HSF.IF.B.5

4) $\frac{y^2+4y}{4y^2-24y+32}\cdot\frac{8y^3-8y^2-16y}{3y^3+12y^2}$  

•  $\frac{8y^2\left(y+1\right)}{12y^2\left(y-4\right)}$  

•  $\frac{8\left(y+1\right)}{12\left(y-4\right)}$  

•  $\frac{2\left(y+1\right)}{3\left(y-4\right)}$  

•  $\frac{2\left(y-2\right)}{3\left(y+4\right)}$  

Tags

CCSS.HSA.APR.D.6

What are the domain restrictions for Problem 4?

•  $y\ne4$ 

•  $y\ne-1,\ 4$ 

•  $y\ne2,\ \pm4$ 

•  $y\ne0,\ 2,\ \pm4$ 

Tags

CCSS.HSA.APR.B.3

5) $\frac{x^2+8x-20}{5x^3+50x^2}\div\frac{x^2+9x}{x^2+7x-18}$  

•  $\frac{1}{5x}$  

•  $\frac{x-2}{5x^3}$  

•  $\frac{x-2}{5x}$  

•  $\frac{\left(x-2\right)^2}{5x^3}$  

Tags

CCSS.HSA.APR.D.6

What are the domain restrictions for Problem 5?

•  $x\ne0$ 

•  $x\ne0,\ 2$ 

•  $x\ne-10,\ -9,\ 0,\ 2$ 

•  $x\ne0,\ 2,\ \pm10$ 

Tags

CCSS.HSA.APR.D.7

CCSS.HSF.IF.B.5