Adding and Subtracting Rational Expressions

Fill in the blank expressions in order to obtain a common denominator. $\frac{2x+1}{\left(x+2\right)\left(x-3\right)}+\frac{x}{\left(x+2\right)\left(\ldots\ldots\ldots\right)}$  

(a)  

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CCSS.HSA.APR.D.7

 $\frac{x-2}{x^2+x-12}-\frac{x}{x^2+6x+8}$  Select the expressions that would make up the Least Common Denominator of the following.

• (x - 3)

• (x - 4)

• (x + 2)

• (x + 4)

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CCSS.HSA.APR.D.7

Simplify the expression. $\frac{2x+1}{x^2-12x+36}+\frac{4x+4}{x^2-12x+36}$  

•  $\frac{6x+5}{x^2-12x+36}$  

• 6x + 5

•  $\frac{8x^2+12x+4}{x^2-12x+36}$  

•  $\frac{x+5}{x^2-2x+36}$  

Tags

CCSS.HSA.APR.D.7

Simplify the expression. $\frac{x-4}{10x+30}-\frac{2}{10x+30}$ 

•  $\frac{x-2}{10x+30}$  

•  $\frac{x-3}{5x+15}$  

•  $\frac{x-6}{10x+30}$  

•  $\frac{x-1}{10x+5}$  

Tags

CCSS.HSA.APR.D.7

Simplify the expression.

 $\frac{x-5}{x-6}+\frac{2}{x+1}$  

•  $\frac{x-7}{\left(x-6\right)\left(x+1\right)}$  

•  $\frac{x^2-2x-17}{\left(x-6\right)\left(x+1\right)}$  

•  $\frac{x-3}{-5}$  

•  $\frac{2x-10}{\left(x+1\right)\left(x-6\right)}$  

Tags

CCSS.HSA.APR.D.7

Simplify the expression. $\frac{3x}{3x-2}-\frac{2}{x+5}$  

•  $\frac{3x^2-21x+4}{\left(3x-2\right)\left(x+5\right)}$  

•  $\frac{3x^2+9x+4}{\left(3x-2\right)\left(x+5\right)}$  

•  $\frac{3x-2}{2x-7}$  

•  $\frac{3x-2}{4x+3}$  

Tags

CCSS.HSA.APR.D.7

Simplify the expression.

 $\frac{4}{x-4}-\frac{3}{x-3}$  

•  $\frac{x}{\left(x-4\right)\left(x-3\right)}$  

•  $\frac{1}{-7}$  

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

•  $\frac{x-24}{\left(x-4\right)\left(x-3\right)}$  

Tags

CCSS.HSA.APR.D.7

Simplify the expression.

 $\frac{2}{x-1}+\frac{4}{x+1}$  

•  $\frac{6x+6}{\left(x-1\right)\left(x+1\right)}$  

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

•  $\frac{6x-2}{2x}$  

•  $\frac{3x-1}{x}$  

Tags

CCSS.HSA.APR.D.7

 $\frac{x}{x+6}+\frac{5x}{x^2+2x-24}$  

•  $\frac{x}{x+4}$  

•  $\frac{6x}{x+6}$  

•  $\frac{6x}{x^2+2x-24}$  

•  $\frac{x^2+x}{\left(x+6\right)\left(x-4\right)}$  

Tags

CCSS.HSA.APR.D.7

Simplify the expression.

 $\frac{2}{x^2-3x+2}-\frac{5x}{x^2-5x+6}$  

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

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

•  $\frac{-5x-2}{-8x+8}$  

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

Tags

CCSS.HSA.APR.D.7