Solve 1/x-y+2/x+y

$$\frac{ 1 }{ x-y } + \frac{ 2 }{ x+y }$$

Evaluate

$$\frac{3x-y}{x^{2}-y^{2}}$$

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{2}{x+y} times \frac{x-y}{x-y}.

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

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

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

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

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

Combine like terms in x+y+2x-2y.

$$\frac{3x-y}{\left(x+y\right)\left(x-y\right)}$$

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

$$\frac{3x-y}{x^{2}-y^{2}}$$

Differentiate w.r.t. x

$$\frac{-3x^{2}+2xy-3y^{2}}{\left(x^{2}-y^{2}\right)^{2}}$$