Solve 4x/x-4-2x^2/x^2-16

$$\frac { 4 x } { x - 4 } - \frac { 2 x ^ { 2 } } { x ^ { 2 } - 16 }$$

Evaluate

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

Short Solution Steps

Factor x^{2}-16.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-4 and \left(x-4\right)\left(x+4\right) is \left(x-4\right)\left(x+4\right). Multiply \frac{4x}{x-4} times \frac{x+4}{x+4}.

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

Since \frac{4x\left(x+4\right)}{\left(x-4\right)\left(x+4\right)} and \frac{2x^{2}}{\left(x-4\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 4x\left(x+4\right)-2x^{2}.

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

Combine like terms in 4x^{2}+16x-2x^{2}.

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

Expand \left(x-4\right)\left(x+4\right).

$$\frac{2x^{2}+16x}{x^{2}-16}$$

Factor

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