Simplify the following rational expression. $\frac { 1 } { x ^ { 2 } - 7 x - 120 } + \frac { 1 } { x ^ { 2 } - 225 } + \frac { 1 } { x ^ { 2 } - 64 }$
A) $\frac { 3 x ^ { 2 } + 7 x - 409 } { ( x - 15 ) ( x + 8 ) }$
B) $\frac { 3 x ^ { 2 } + 7 x - 409 } { ( x - 15 ) ( x + 15 ) ( x + 8 ) ( x - 8 ) }$
C) $\frac { 3 x ^ { 2 } + 7 x } { ( x + 15 ) ( x + 8 ) ( x - 8 ) }$
D) $\frac { 3 } { ( x - 15 ) ( x + 15 ) ( x + 8 ) ( x - 8 ) }$
E) $\frac { 7 x - 409 } { ( x - 15 ) ( x + 15 ) ( x + 8 ) ( x - 8 ) }$

Question

Quizplus · Accepted Answer

To simplify the given expression, factor each denominator: $x^2 - 7x - 120 = (x - 15)(x + 8)$, $x^2 - 225 = (x - 15)(x + 15)$, and $x^2 - 64 = (x - 8)(x + 8)$. The least common denominator (LCD) is $(x - 15)(x + 15)(x + 8)(x - 8)$. Simplifying the expression with this LCD results in a numerator that combines the terms appropriately, leading to choice B as the correct answer.

Simplify the Following Rational Expression 1x2−7x−120+1x2−225+1x2−64\frac { 1 } { x ^ { 2 } - 7 x - 120 } + \frac { 1 } { x ^ { 2 } - 225 } + \frac { 1 } { x ^ { 2 } - 64 }x2−7x−1201​+x2−2251​+x2−641​

Simplify the Following Rational Expression $\frac { 1 } { x ^ { 2 } - 7 x - 120 } + \frac { 1 } { x ^ { 2 } - 225 } + \frac { 1 } { x ^ { 2 } - 64 }$