Solve 1/x+y+1/x-y

$$\frac{ 1 }{ x+y } + \frac{ 1 }{ x-y }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+y and x-y is \left(x+y\right)\left(x-y\right). Multiply \frac{1}{x+y} times \frac{x-y}{x-y}. Multiply \frac{1}{x-y} times \frac{x+y}{x+y}.

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

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

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

Combine like terms in x-y+x+y.

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

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

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

Differentiate w.r.t. x

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