Solve x^2+x-20/8x*2x+8/x^2-16

$$\frac { x ^ { 2 } + x - 20 } { 8 x } \times \frac { 2 x + 8 } { x ^ { 2 } - 16 }$$

Evaluate

$$\frac{1}{4}+\frac{5}{4x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x+8}{x^{2}-16}.

$$\frac{x^{2}+x-20}{8x}\times \frac{2\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{x^{2}+x-20}{8x}\times \frac{2}{x-4}$$

Multiply \frac{x^{2}+x-20}{8x} times \frac{2}{x-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+x-20\right)\times 2}{8x\left(x-4\right)}$$

Cancel out 2 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-4 in both numerator and denominator.

$$\frac{x+5}{4x}$$

Expand

$$\frac{1}{4}+\frac{5}{4x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x+8}{x^{2}-16}.

$$\frac{x^{2}+x-20}{8x}\times \frac{2\left(x+4\right)}{\left(x-4\right)\left(x+4\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{x^{2}+x-20}{8x}\times \frac{2}{x-4}$$

Multiply \frac{x^{2}+x-20}{8x} times \frac{2}{x-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+x-20\right)\times 2}{8x\left(x-4\right)}$$

Cancel out 2 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-4 in both numerator and denominator.

$$\frac{x+5}{4x}$$