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

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

Evaluate

$$\frac{2\left(3x-8\right)}{x^{2}-16}$$

Short Solution Steps

Factor x^{2}-16.

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

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{4}{x+4} times \frac{x-4}{x-4}.

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

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

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

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

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

Combine like terms in 4x-16+2x.

$$\frac{6x-16}{\left(x-4\right)\left(x+4\right)}$$

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

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

Factor

$$\frac{2\left(3x-8\right)}{x^{2}-16}$$