Solve 8x/x^2-16div2x/x+4

$$\frac { 8 x } { x ^ { 2 } - 16 } \div \frac { 2 x } { x + 4 }$$

Evaluate

$$\frac{4}{x-4}$$

Short Solution Steps

Divide \frac{8x}{x^{2}-16} by \frac{2x}{x+4} by multiplying \frac{8x}{x^{2}-16} by the reciprocal of \frac{2x}{x+4}.

$$\frac{8x\left(x+4\right)}{\left(x^{2}-16\right)\times 2x}$$

Cancel out 2x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+4 in both numerator and denominator.

$$\frac{4}{x-4}$$

Differentiate w.r.t. x

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