Solve x-a/x+a+x+a/(x-a)=

$$\frac { x - a } { x + a } + \frac { x + a } { ( x - a ) } =$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in x^{2}-xa-xa+a^{2}+x^{2}+xa+xa+a^{2}.

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

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

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in x^{2}-xa-xa+a^{2}+x^{2}+xa+xa+a^{2}.

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

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

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