Solve 1/x^2-16+1/2x-8

$$\frac { 1 } { x ^ { 2 } - 16 } + \frac { 1 } { 2 x - 8 }$$

Evaluate

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

Short Solution Steps

Factor x^{2}-16. Factor 2x-8.

$$\frac{1}{\left(x-4\right)\left(x+4\right)}+\frac{1}{2\left(x-4\right)}$$

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 2\left(x-4\right) is 2\left(x-4\right)\left(x+4\right). Multiply \frac{1}{\left(x-4\right)\left(x+4\right)} times \frac{2}{2}. Multiply \frac{1}{2\left(x-4\right)} times \frac{x+4}{x+4}.

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

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

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

Combine like terms in 2+x+4.

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

Expand 2\left(x-4\right)\left(x+4\right).

$$\frac{6+x}{2x^{2}-32}$$

Factor

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