Solve x^3+125/x^2-49divx^3-5x^2+25x/{x^2+x-56}

$$\frac{ { x }^{ 3 } +125 }{ { x }^{ 2 } -49 } \div \frac{ { x }^{ 3 } -5 { x }^{ 2 } +25x }{ { x }^{ 2 } +x-56 }$$

Evaluate

$$\frac{\left(x+5\right)\left(x+8\right)}{x\left(x+7\right)}$$

Short Solution Steps

Divide \frac{x^{3}+125}{x^{2}-49} by \frac{x^{3}-5x^{2}+25x}{x^{2}+x-56} by multiplying \frac{x^{3}+125}{x^{2}-49} by the reciprocal of \frac{x^{3}-5x^{2}+25x}{x^{2}+x-56}.

$$\frac{\left(x^{3}+125\right)\left(x^{2}+x-56\right)}{\left(x^{2}-49\right)\left(x^{3}-5x^{2}+25x\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x+5\right)\left(x+8\right)\left(x^{2}-5x+25\right)}{x\left(x-7\right)\left(x+7\right)\left(x^{2}-5x+25\right)}$$

Cancel out \left(x-7\right)\left(x^{2}-5x+25\right) in both numerator and denominator.

$$\frac{\left(x+5\right)\left(x+8\right)}{x\left(x+7\right)}$$

Expand the expression.

$$\frac{x^{2}+13x+40}{x^{2}+7x}$$

Expand

$$\frac{x^{2}+13x+40}{x\left(x+7\right)}$$

Short Solution Steps

Divide \frac{x^{3}+125}{x^{2}-49} by \frac{x^{3}-5x^{2}+25x}{x^{2}+x-56} by multiplying \frac{x^{3}+125}{x^{2}-49} by the reciprocal of \frac{x^{3}-5x^{2}+25x}{x^{2}+x-56}.

$$\frac{\left(x^{3}+125\right)\left(x^{2}+x-56\right)}{\left(x^{2}-49\right)\left(x^{3}-5x^{2}+25x\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-7\right)\left(x+5\right)\left(x+8\right)\left(x^{2}-5x+25\right)}{x\left(x-7\right)\left(x+7\right)\left(x^{2}-5x+25\right)}$$

Cancel out \left(x-7\right)\left(x^{2}-5x+25\right) in both numerator and denominator.

$$\frac{\left(x+5\right)\left(x+8\right)}{x\left(x+7\right)}$$

Expand the expression.

$$\frac{x^{2}+13x+40}{x^{2}+7x}$$