Add or subtract.
-$\frac { 5 y } { x ^ { 2 } - y ^ { 2 } } + \frac { 5 x } { y ^ { 2 } - x ^ { 2 } }$
A) $\frac { 5 } { x - y }$
B) $- \frac { 5 } { x + y }$
C) $\frac { 5 } { x + y }$
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 $\frac{5y}{x^2 - y^2} - \frac{5x}{x^2 - y^2}$, which simplifies further to $-\frac{5(x+y)}{x^2 - y^2}$. Since $x^2 - y^2 = (x+y)(x-y)$, the expression becomes $-\frac{5}{x+y}$.

Add or Subtract 5yx2−y2+5xy2−x2\frac { 5 y } { x ^ { 2 } - y ^ { 2 } } + \frac { 5 x } { y ^ { 2 } - x ^ { 2 } }x2−y25y​+y2−x25x​

Add or Subtract $\frac { 5 y } { x ^ { 2 } - y ^ { 2 } } + \frac { 5 x } { y ^ { 2 } - x ^ { 2 } }$