Divide.
-$\frac { ( p - q ) ^ { 2 } } { ( p + q ) ^ { 2 } } \div \frac { p ^ { 2 } - 2 p q + q ^ { 2 } } { p ^ { 2 } - q ^ { 2 } }$
A) $\frac { p ^ { 2 } - 2 p q + q ^ { 2 } } { ( p + q ) ^ { 2 } }$
B) $\frac { p - q } { p + q }$
C) $\frac { p + q } { p - q }$
D) $- 2 p q$

Question

Quizplus · Accepted Answer

The division of the given fractions simplifies to $\frac{(p-q)^2}{(p+q)^2} \times \frac{p^2-q^2}{p^2-2pq+q^2}$. Recognizing that $(p-q)^2 = p^2 - 2pq + q^2$ and $(p+q)^2 = p^2 + 2pq + q^2$, and that $p^2 - q^2 = (p+q)(p-q)$, the expression simplifies to $\frac{p-q}{p+q}$, which is option B.

Divide - (p−q)2(p+q)2÷p2−2pq+q2p2−q2\frac { ( p - q ) ^ { 2 } } { ( p + q ) ^ { 2 } } \div \frac { p ^ { 2 } - 2 p q + q ^ { 2 } } { p ^ { 2 } - q ^ { 2 } }(p+q)2(p−q)2​÷p2−q2p2−2pq+q2​

Divide
- $\frac { ( p - q ) ^ { 2 } } { ( p + q ) ^ { 2 } } \div \frac { p ^ { 2 } - 2 p q + q ^ { 2 } } { p ^ { 2 } - q ^ { 2 } }$