Perform the indicated operation. Simplify if possible.
-$\frac { 10 } { 3 x - 9 } + \frac { x } { x ^ { 2 } - 9 }$
A) $\frac { x + 10 } { 3 ( x + 3 ) ( x - 3 ) }$
B) $\frac { 13 x + 30 } { 3 ( x + 3 ) ( x - 3 ) }$
C) $\frac { 11 x + 30 } { ( x + 3 ) ( x - 3 ) }$
D) $\frac { 13 x } { ( x + 3 ) ( x - 3 ) }$

Question

Quizplus · Accepted Answer

First, factor the denominators: $3x - 9 = 3(x - 3)$ and $x^2 - 9 = (x + 3)(x - 3)$. The common denominator is $3(x + 3)(x - 3)$. Rewrite each fraction with the common denominator and simplify: $\frac{10}{3(x - 3)} + \frac{x}{(x + 3)(x - 3)} = \frac{10(x + 3)}{3(x + 3)(x - 3)} + \frac{3x}{3(x + 3)(x - 3)} = \frac{10x + 30 + 3x}{3(x + 3)(x - 3)} = \frac{13x + 30}{3(x + 3)(x - 3)}$.

Perform the Indicated Operation 103x−9+xx2−9\frac { 10 } { 3 x - 9 } + \frac { x } { x ^ { 2 } - 9 }3x−910​+x2−9x​

Perform the Indicated Operation $\frac { 10 } { 3 x - 9 } + \frac { x } { x ^ { 2 } - 9 }$