Rewrite the rational expression as an equivalent rational expression with the given denominator.
-$\frac { a } { a + 5 b } = \frac { } { a ^ { 2 } - 25 b ^ { 2 } }$
A) $\frac { a } { a ^ { 2 } - 25 b ^ { 2 } }$
B) $\frac { a ^ { 2 } - b ^ { 2 } } { a ^ { 2 } - 25 b ^ { 2 } }$
C) $\frac { a ^ { 2 } - 5 a b } { a ^ { 2 } - 25 b ^ { 2 } }$
D) $\frac { 5 a b } { a ^ { 2 } - 25 b ^ { 2 } }$

Question

Quizplus · Accepted Answer

The given denominator $a^2 - 25b^2$ is a difference of squares and can be factored into $(a + 5b)(a - 5b)$. The original denominator is $a + 5b$, so to get an equivalent expression with the new denominator, multiply the numerator and the original denominator by $a - 5b$. This gives $\frac{a(a - 5b)}{(a + 5b)(a - 5b)} = \frac{a^2 - 5ab}{a^2 - 25b^2}$.

Rewrite the Rational Expression as an Equivalent Rational Expression with the Given