$$\frac { 1 } { a + b } + \frac { 1 } { a - b } + \frac { 2 b } { a ^ { 2 } - b ^ { 2 } }$$
Evaluate
$\frac{2}{a-b}$
Short Solution Steps
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $a+b$ and $a-b$ is $\left(a+b\right)\left(a-b\right)$. Multiply $\frac{1}{a+b}$ times $\frac{a-b}{a-b}$. Multiply $\frac{1}{a-b}$ times $\frac{a+b}{a+b}$.
Since $\frac{a-b}{\left(a+b\right)\left(a-b\right)}$ and $\frac{a+b}{\left(a+b\right)\left(a-b\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{2a}{\left(a+b\right)\left(a-b\right)}$ and $\frac{2b}{\left(a+b\right)\left(a-b\right)}$ have the same denominator, add them by adding their numerators.
