$$\frac { 1 } { x + 2 y } + \frac { 1 } { x - 2 y } + \frac { 2 x } { 4 y ^ { 2 } - x ^ { 2 } }$$
Evaluate
$0$
Short Solution Steps
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x+2y$ and $x-2y$ is $\left(x-2y\right)\left(x+2y\right)$. Multiply $\frac{1}{x+2y}$ times $\frac{x-2y}{x-2y}$. Multiply $\frac{1}{x-2y}$ times $\frac{x+2y}{x+2y}$.
Since $\frac{x-2y}{\left(x-2y\right)\left(x+2y\right)}$ and $\frac{x+2y}{\left(x-2y\right)\left(x+2y\right)}$ have the same denominator, add them by adding their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x-2y\right)\left(x+2y\right)$ and $\left(x+2y\right)\left(-x+2y\right)$ is $\left(x+2y\right)\left(-x+2y\right)$. Multiply $\frac{2x}{\left(x-2y\right)\left(x+2y\right)}$ times $\frac{-1}{-1}$.
Since $\frac{-2x}{\left(x+2y\right)\left(-x+2y\right)}$ and $\frac{2x}{\left(x+2y\right)\left(-x+2y\right)}$ have the same denominator, add them by adding their numerators.
