Adding and Subtracting Rational Expressions

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.6

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.6

CCSS.HSA.APR.D.7

Subtract
 $\frac{x}{2x+3}-\frac{2x+1}{2x-3}$  

•  $\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)};\ x\ne\pm\frac{2}{3}$  

•  $\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)};\ x\ne\pm\frac{3}{2}$  

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

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

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Subtract
 $\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}$  

•  $\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)};\ x\ne-8,\ 4$  

•  $\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)};\ x\ne-4,\ 8$  

•  $\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)};\ x\ne-8,\ 4$  

•  $\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)};\ x\ne-4,\ 8$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

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.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

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

CCSS.HSA.APR.D.7

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.6

CCSS.HSA.APR.D.7

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

•  $\frac{4x-6}{4x-7};\ x\ne-\frac{7}{4}$  

•  $\frac{4x^2-6x+9}{4x-7};\ x\ne\frac{7}{4}$  

•  $\frac{4x-6}{4x-7};\ x\ne\frac{7}{4}$  

•  $\frac{4x-6}{8x-14};\ x\ne-\frac{14}{8}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

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.6

CCSS.HSA.APR.D.7

Add
 $\frac{2}{x^2-x-20}+\frac{3}{x^2+7x+12}$  

•  $\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)};\ x\ne-5,\ 3\ 4$  

•  $\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)};\ x\ne-4,-3,\ 5$  

•  $\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)};\ x\ne-5,\ 3\ 4$  

•  $\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)};\ x\ne-4,-3\ 5$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3