Solve n/n-x+n/n+x

$$\frac { n } { n - x } + \frac { n } { n + x }$$

Evaluate

$$\frac{2n^{2}}{n^{2}-x^{2}}$$

Short Solution Steps

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

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

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

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

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

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

Combine like terms in nx+n^{2}-nx+n^{2}.

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

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

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

Factor

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