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

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

Evaluate

$$\frac{x\left(x+6\right)}{x^{2}-16}$$

Short Solution Steps

Factor x^{2}-16.

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

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

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

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

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

Do the multiplications in 2x+x\left(x+4\right).

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

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

$$\frac{6x+x^{2}}{\left(x-4\right)\left(x+4\right)}$$

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

$$\frac{6x+x^{2}}{x^{2}-16}$$

Factor

$$\frac{x\left(x+6\right)}{x^{2}-16}$$