Complex Rational expressions

Simplify: $\frac{\frac{x}{x-1}+\frac{3}{x+5}}{\frac{5}{x+5}-\frac{x}{x-1}}$  

•  $\frac{x^2+2x+15}{-x^2-5}$  

•  $\frac{x^2+8x-3}{x^2+10x-5}$  

•  $\frac{x^2+2x+15}{x^2+10x-5}$  

•  $\frac{x^2+8x-3}{-x^2-5}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Simplify: $\frac{\frac{1}{k+2}}{\frac{5}{k^2-4}}$  

•  $\frac{k-2}{5}$  

•  $\frac{k+2}{5}$  

•  $\frac{5}{k-2}$  

•  $k-2$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify: $\frac{\frac{6-y}{6}}{\frac{1}{6}-\frac{1}{y}}$  

• -y

• y

•  $-\frac{6}{y}$  

•  $-\frac{1}{y}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Simplify:  $\frac{\frac{x}{5}}{\frac{4}{x+6}}$  

•  $\frac{4x}{5\left(x+6\right)}$  

•  $20x\left(x+6\right)$  

•  $\frac{x\left(x+6\right)}{20}$  

•  $\frac{x+6}{20x}$  

simplify:  $\frac{\frac{10}{x+1}}{\frac{1}{2}+\frac{3}{x+1}}$  

•  $\frac{20x}{x+7}$  

•  $\frac{20}{x+7}$  

•  $\frac{10}{x+7}$  

•  $\frac{10\left(x+7\right)}{x+1}$  

simplify: $\frac{\frac{x}{25}+\frac{x}{5}}{\frac{5}{x}}$  

•  $\frac{25x^2}{400+4x}$  

•  $\frac{6x^2}{125}$  

•  $\frac{400x}{x^3-16}$  

•  $\frac{x^2+x^3}{625}$  

Simplify: $\frac{\frac{20}{x}-\frac{25}{2x}}{\frac{5}{x^2}+\frac{1}{8}}$  

•  $\frac{16x-100}{25x}$  

•  $\frac{5x^2-1250}{2x^2+25x}$  

•  $\frac{60x}{40+x^2}$  

•  $-\frac{93x}{125x-800}$  

Simplify: $\frac{\frac{4}{x-2}-\frac{x}{16}}{\frac{x^2}{2x-4}+\frac{x-2}{4}}$  

•  $\frac{x-2}{x-6}$  

•  $\frac{12x-32+2x^2}{66x-x^2}$  

•  $\frac{64-x^2+2x}{12x^2-16x+16}$  

•  $\frac{20x-24-4x^2}{x+30}$  

Simplify: $\frac{\frac{1}{k+3}}{\frac{7k^2}{k^2+7k+12}}$  

• k + 3

• k - 10

•  $\frac{k-5}{3}$  

•  $\frac{k+4}{7k^2}$  

Simplify: $\frac{\frac{5k^3-25k^2}{5k^2}}{\frac{k^2+2k-35}{9}}$  

•  $\frac{4k^2}{k-7}$  

•  $\frac{9}{k+7}$  

•  $\frac{9}{4}$  

• 1