Solve 2x^3+10x^2/x^2+x-20div4x/x-4

$$\frac { 2 x ^ { 3 } + 10 x ^ { 2 } } { x ^ { 2 } + x - 20 } \div \frac { 4 x } { x - 4 }$$

Evaluate

$$\frac{x}{2}$$

Short Solution Steps

Divide \frac{2x^{3}+10x^{2}}{x^{2}+x-20} by \frac{4x}{x-4} by multiplying \frac{2x^{3}+10x^{2}}{x^{2}+x-20} by the reciprocal of \frac{4x}{x-4}.

$$\frac{\left(2x^{3}+10x^{2}\right)\left(x-4\right)}{\left(x^{2}+x-20\right)\times 4x}$$

Factor the expressions that are not already factored.

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

Cancel out 2x\left(x-4\right)\left(x+5\right) in both numerator and denominator.

$$\frac{x}{2}$$

Expand

$$\frac{x}{2}$$

Short Solution Steps

Divide \frac{2x^{3}+10x^{2}}{x^{2}+x-20} by \frac{4x}{x-4} by multiplying \frac{2x^{3}+10x^{2}}{x^{2}+x-20} by the reciprocal of \frac{4x}{x-4}.

$$\frac{\left(2x^{3}+10x^{2}\right)\left(x-4\right)}{\left(x^{2}+x-20\right)\times 4x}$$

Factor the expressions that are not already factored.

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

Cancel out 2x\left(x-4\right)\left(x+5\right) in both numerator and denominator.

$$\frac{x}{2}$$