Perform the indicated operation. If possible, simplify your answer.
-$$\frac { 6 } { x ^ { 2 } - x - 30 } + \frac { 5 } { x ^ { 2 } - 11 x + 30 }$$
A) $\frac { 11 x - 5 } { ( x + 6 ) ( x + 5 ) ( x - 5 ) }$
B) $\frac { 11 x - 5 } { ( x - 6 ) ( x + 5 ) ( x - 5 ) }$
C) $\frac { 9 x - 5 } { ( x - 6 ) ( x + 5 ) ( x - 5 ) }$
D) $\frac { 9 x - 5 } { ( x + 6 ) ( x + 5 ) ( x - 5 ) }$

Question

Quizplus · Accepted Answer

First, factor the denominators: $x^2 - x - 30 = (x - 6)(x + 5)$ and $x^2 - 11x + 30 = (x - 6)(x - 5)$. To add the fractions, find a common denominator, which is $(x - 6)(x + 5)(x - 5)$. Adjust the numerators accordingly and simplify to get $\frac{11x - 5}{(x - 6)(x + 5)(x - 5)}$.

Perform the Indicated Operation 6x2−x−30+5x2−11x+30\frac { 6 } { x ^ { 2 } - x - 30 } + \frac { 5 } { x ^ { 2 } - 11 x + 30 }x2−x−306​+x2−11x+305​

Perform the Indicated Operation $\frac { 6 } { x ^ { 2 } - x - 30 } + \frac { 5 } { x ^ { 2 } - 11 x + 30 }$