Perform the operations and simplify. $$\frac { 1 } { x - 6 } + \frac { 3 } { x + 6 } - \frac { 3 x - 6 } { x ^ { 2 } - 36 }$$
Assume that no denominators are 0 .
A) $\frac { 1 } { x - 6 }$
B) $\frac { 1 } { x + 36 }$
C) $\frac { 1 } { x + 6 }$
D) $\frac { 6 } { x + 6 }$

Question

Quizplus · Accepted Answer

To add the fractions, we need a common denominator. The denominator of the first fraction is $(x - 6)$, the denominator of the second fraction is $(x + 6)$, and the denominator of the third fraction is $(x^2 - 36) = (x+6)(x-6)$. So we have:

\begin{align*}
\frac{1}{x-6} + \frac{3}{x+6} - \frac{3x-6}{x^2-36} &= \frac{(x+6)}{(x-6)(x+6)} + \frac{(3)(x-6)}{(x+6)(x-6)}  - \frac{(3x-6)}{(x+6)(x-6)} \
&= \frac{(x+6) + 3(x-6) - (3x-6)}{(x+6)(x-6)} \
&= \frac{x-3}{(x+6)(x-6)} \
&= \frac{1}{x-6} - \frac{1}{x+6}
\end{align*}

Thus, the simplified expression is $\frac{1}{x-6} - \frac{1}{x+6}$, which is equivalent to $\frac{1}{x+6} - \frac{1}{x-6}$. We can see that the only answer choice that matches this is C.

Perform the Operations and Simplify 1x−6+3x+6−3x−6x2−36\frac { 1 } { x - 6 } + \frac { 3 } { x + 6 } - \frac { 3 x - 6 } { x ^ { 2 } - 36 }x−61​+x+63​−x2−363x−6​

Perform the Operations and Simplify $\frac { 1 } { x - 6 } + \frac { 3 } { x + 6 } - \frac { 3 x - 6 } { x ^ { 2 } - 36 }$