For all \(x\neq \pm y\), \(\dfrac{x}{x+y}+\dfrac{y}{x-y}\) = ?

Summary Submit Skip Question

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