Add or subtract as indicated. Simplify the result, if possible.
-$$\frac { 2 y } { x ^ { 2 } - y ^ { 2 } } + \frac { 2 x } { y ^ { 2 } - x ^ { 2 } }$$
A) $\frac { 2 } { x - y }$
B) $- \frac { 2 } { x + y }$
C) $\frac { 2 } { x + y }$
D) $\frac { y - x } { x ^ { 2 } - y ^ { 2 } }$

Question

Quizplus · Accepted Answer

The denominators $x^2 - y^2$ and $y^2 - x^2$ are opposites, so $y^2 - x^2 = -(x^2 - y^2)$. Thus, the expression simplifies to $\frac{2y}{x^2 - y^2} - \frac{2x}{x^2 - y^2}$, which further simplifies to $-\frac{2(x+y)}{x^2 - y^2}$. Since $x^2 - y^2 = (x+y)(x-y)$, the expression simplifies to $-\frac{2}{x+y}$.

Add or Subtract as Indicated 2yx2−y2+2xy2−x2\frac { 2 y } { x ^ { 2 } - y ^ { 2 } } + \frac { 2 x } { y ^ { 2 } - x ^ { 2 } }x2−y22y​+y2−x22x​

Add or Subtract as Indicated $\frac { 2 y } { x ^ { 2 } - y ^ { 2 } } + \frac { 2 x } { y ^ { 2 } - x ^ { 2 } }$