Adding and Subtracting Rationals

Find the least common denominator of the expression

• 18
• 6x
• 3xy
• 6xy

Tags

CCSS.HSA.APR.D.7

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CCSS.HSA.APR.D.7

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CCSS.HSA.APR.D.7

Subtract
 $\frac{x-5}{3x+4}-\frac{3x-5}{3x+4}$  

•  $\frac{-2x-10}{3x+4};\ x\ne-\frac{4}{3}$  

•  $\frac{-2x}{3c+4};\ x\ne-\frac{4}{3}$  

•  $-2x;\ x\ne0$  

•  $-2x-10;\ x\ne0$  

Tags

CCSS.HSA.APR.D.7

Add
 $\frac{3x-2}{x+2}+\frac{2x}{4x-1}$  

•  $\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}$  

•  $\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ 1$  

•  $\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}$  

•  $\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-\frac{1}{4},\ 2$  

Tags

CCSS.HSA.APR.D.7

Subtract
 $\frac{x^2-3}{2x+7}-\frac{2x-5}{2x+7}$  

•  $\frac{x^2-2x-8}{2x+7};\ x\ne-\frac{7}{2}$  

•  $x^2-2x-8;\ x\ne0$  

•  $x^2-2x+2;\ x\ne0$  

•  $\frac{x^2-2x+2}{2x+7};\ x\ne-\frac{7}{2}$  

Tags

CCSS.HSA.APR.D.7

Simplify (add & divide)
 $\frac{\frac{1}{2x}+\frac{2}{3x}}{\frac{x-1}{x-3}}$  

•  $\frac{7x-21}{6x^2-6x};\ x\ne0,\ 1,\ 3$  

•  $\frac{7x-21}{6x^2-6x};\ x\ne1,\ 3$  

•  $\frac{7x^2-21x}{6x^3-6x^2};\ x\ne0,\ 1,\ 3$  

•  $\frac{7x^2-21x}{6x^3-6x^2};\ x\ne1,\ 3$  

Tags

CCSS.HSA.APR.D.6

Add
 $\frac{7x}{x^2-5x}+\frac{x^2}{x-5}$  

•  $\frac{x^3+7x}{x\left(x-5\right)};\ x\ne5$  

•  $\frac{x^2+7}{x-5};\ x\ne0,\ 5$  

•  $\frac{x^4-5x^3+7x^2-35x}{\left(x^2-5x\right)\left(x-5\right)};\ x\ne5$  

•  $\frac{x^4-5x^3+7x^2-35x}{\left(x^2-5x\right)\left(x-5\right)};\ x\ne0,\ 5$  

Tags

CCSS.HSA.APR.D.7

Add
 $\frac{2x}{x^2-36}+\frac{x+4}{x+6}$  

•  $\frac{x^2-24}{\left(x+6\right)\left(x-6\right)};\ x\ne\pm6$  

•  $\frac{x^3+6x^2-24x}{\left(x+6\right)\left(x^2-36\right)};\ x\ne-6,\ 36$  

•  $\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)};\ x\ne\pm6$  

•  $\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)};\ x\ne\pm6$  

Tags

CCSS.HSA.APR.D.7

Simplify 

 $\frac{m}{3m+6}-\frac{4m}{m+2}$  

•  $-\frac{11m}{3\left(m+2\right)},m\ne-2$  

•  $\frac{13m}{3\left(m+2\right)},m\ne0,-2$  

•  $\frac{m}{3\left(m+2\right)^2},m\ne0,-2$  

•  $-\frac{3m}{m+2},m\ne-2$  

Tags

CCSS.HSA.APR.D.7