Operations with Rational Expressions

Simplify  $\frac{\left(x^2-10x+16\right)}{x-8}\cdot\frac{\left(6x^4+66x^3+108x^2\right)}{6x^2-24}$  

•  $\frac{\left(6x^2\left(x+9\right)\right)}{6}$  

•  $x^2\left(x+9\right)$  

•  $\frac{\left(6x^2-60x+96\right)}{6}$  

•  $\frac{\left(6x^3+54x^2\right)}{6}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

 $\frac{2}{5x}+\frac{1}{x}$  

Simplify

•  $\frac{3}{6x}$  

•  $\frac{1}{2x}$  

•  $\frac{7}{5x}$  

•  $\frac{3}{5x}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

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

Simplify

•  $\frac{\left(-5x+5\right)}{3}$  

•  $\frac{\left(-3x+5\right)}{3}$  

•  $-x+\frac{5}{3}$  

•  $\frac{\left(-3x+1\right)}{3}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

 $\frac{\left(5x+1\right)}{\left(x-6\right)}-\frac{x}{x^2-10x+24}$  

Simplify

•  $\frac{\left(5x^2-20x-4\right)}{\left(x+4\right)\left(x-6\right)}$  

•  $\frac{\left(5x^2-20x-4\right)}{\left(x-4\right)\left(x-6\right)}$  

•  $5x^2-20x-4$  

•  $\frac{\left(4x+1\right)}{\left(x-4\right)\left(x-6\right)}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

 $\frac{\left(7x+2\right)}{x-6}+\frac{5}{6-x}$  

Simplify

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

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

•  $-\frac{\left(7x-3\right)}{\left(x-6\right)}$  

•  $\frac{\left(7x-3\right)}{\left(x-6\right)}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $3x^2-20x+25$  

Factor

•  $\left(x-5\right)\left(x-15\right)$  

•  $\left(3x-5\right)\left(x+15\right)$  

•  $\left(3x-5\right)\left(x-5\right)$  

•  $\left(3x+5\right)\left(x-5\right)$  

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $6x^2+17x-14$  

Factor

•  $\left(3x-2\right)\left(2x+7\right)$  

•  $\left(6x-7\right)\left(x+2\right)$  

•  $\left(3x+2\right)\left(2x-7\right)$  

•  $\left(3x+7\right)\left(2x-2\right)$  

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\frac{\left(x^2+5x-6\right)}{x^2-10x+9}$  

Simplify

•  $\frac{\left(x-1\right)\left(x+6\right)}{\left(x-1\right)\left(x+9\right)}$  

• cannot be simplified

•  $\frac{5x}{3}$  

•  $\frac{\left(x+6\right)}{\left(x-9\right)}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

 $\frac{7x}{x-8}\div\frac{\left(x^2+4x-32\right)}{x^2-64}$  

Simplify

•  $\frac{7x}{\left(x-4\right)}$  

•  $7x^3-448x^2$  

•  $\frac{7x\left(x+8\right)\left(x^2+4x-32\right)}{\left(x-8\right)\left(x+8\right)}$  

•  $\left(x-8\right)$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

 $\frac{\left(x^2-6x-16\right)}{x}\cdot\frac{2x}{x^2-4}$  

Simplify

•  $\frac{2x\left(x-8\right)}{x\left(x-2\right)}$  

•  $\frac{\left(2x^2-16x\right)}{x^2-2x}$  

•  $\frac{2\left(x-8\right)}{x-2}$  

•  $\frac{\left(2x-4\right)}{x-1}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7