Find the least common denominator of the rational expressions.
-$\frac { 15 } { x ^ { 2 } + 2 x - 15 }$ and $\frac { 4 x - 20 } { - 4 x - 20 }$
A) $- 4 ( x - 3 ) ( x - 5 )$
B) $- 4 ( x - 3 ) ( x + 5 )$
C) $- 4 ( x + 3 ) ( x - 5 )$
D) $- 4 ( x + 3 ) ( x + 5 )$

Question

Quizplus · Accepted Answer

First, factor each denominator. $x^2 + 2x - 15$ factors into $(x + 5)(x - 3)$. The second denominator, $-4x - 20$, can be factored as $-4(x + 5)$. The least common denominator (LCD) must include each factor the greatest number of times it occurs in any of the denominators. Thus, the LCD is $-4(x + 5)(x - 3)$, which matches choice B.

Find the Least Common Denominator of the Rational Expressions 15x2+2x−15\frac { 15 } { x ^ { 2 } + 2 x - 15 }x2+2x−1515​

Find the Least Common Denominator of the Rational Expressions $\frac { 15 } { x ^ { 2 } + 2 x - 15 }$