8.5B Adding/Subtracting Rational Expressions Worksheet

1. Simplify each expression:

 $\frac{-2}{n+4}-\frac{n^2}{n^2-16}$  

•  $\frac{-\left(n-2\right)}{n-4}$  

•  $\frac{-\left(n^2+2\right)}{n^2+n-12}$  

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

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

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

1. State any restrictions on the variables:

 $\frac{-2}{n+4}-\frac{n^2}{n^2-16}$  

•  $n\ne2,\pm4$  

•  $n\ne2,4$  

•  $n\ne\pm4$  

•  $n\ne4$  

Tags

CCSS.HSA.CED.A.3

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

2. State any restrictions on the variables:

 $\frac{3^2}{8x^3y^3}-\frac{1}{4xy}$  

•  $x\ne0,\ y\ne0$  

•  $x\ne2,\ y\ne2$  

•  $x\ne8,\ y\ne4$  

• No restrictions

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.CED.A.3

3. Simplify each expression:

 $\frac{6}{5x^2y}+\frac{5}{10xy^2}$  

•  $\frac{5x+12y}{10x^2y^2}$  

•  $\frac{11}{10x^2y^2}$  

•  $\frac{11}{50x^3y^3}$  

•  $\frac{5x+12y}{50x^3y^3}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

3. State any restrictions on the variables:

 $\frac{6}{5x^2y}+\frac{5}{10xy^2}$  

•  $x\ne5,\ y\ne5$  

•  $x\ne6,\ y\ne5$  

•  $x\ne0,\ y\ne0$  

•  $x\ne5,\ y\ne6$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSA.CED.A.3

4. Simplify each expression:  $\frac{x+2}{x^2+4x+4}+\frac{2}{x+2}$  

•  $\frac{2}{x+2}$  

•  $\frac{4}{x+2}$  

•  $\frac{3}{x+2}$  

•  $\frac{1}{x+2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

4. State any restrictions on the variables:  $\frac{x+2}{x^2+4x+4}+\frac{2}{x+2}$  

•  $x\ne\pm2$  

•  $x\ne-4$  

•  $x\ne\pm4$  

•  $x\ne-2$  

Tags

CCSS.HSA.APR.D.7

5. Simplify each expression:  $\frac{4}{x^2-25}+\frac{6}{x^2+6x+5}$  

•  $\frac{10}{\left(x+1\right)\left(x+5\right)\left(x-5\right)}$  

•  $\frac{2\left(5x-13\right)}{\left(x+1\right)\left(x+5\right)\left(x-5\right)}$  

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

•  $\frac{10x-1}{\left(x+5\right)\left(x-5\right)}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

5. State any restrictions on the variables:  $\frac{4}{x^2-25}+\frac{6}{x^2+6x+5}$  

•  $x\ne-1,\pm5$  

•  $x\pm-4,-6$  

•  $x\ne5,-4,-6$  

•  $x\ne0,5$  

Tags

CCSS.HSA.APR.D.7