Perform the operations and simplify. $$\frac { x + 3 } { x ^ { 2 } + 9 x + 18 } + \frac { x } { x ^ { 2 } - 36 }$$
Assume that no denominators are 0 .
A) $\quad \frac { 2 x - 36 } { x ^ { 2 } - 36 }$
B) $\quad \frac { 2 x - 36 } { x ^ { 2 } - 6 }$
C) $\quad \frac { 2 x + 6 } { x ^ { 2 } - 36 }$
D) $\frac { 2 x - 6 } { x ^ { 2 } - 36 }$

Question

Quizplus · Accepted Answer

To add fractions, we need a common denominator. Factoring the denominators, we get 
$$x^{2}+9x+18=(x+6)(x+3)$$$$x^{2}-36=(x+6)(x-6)$$
So the common denominator is $(x+6)(x+3)(x-6)$. Then we have 
\begin{align*}
\frac{x+3}{x^{2}+9x+18}+\frac{x}{x^{2}-36}&=\frac{x+3}{(x+6)(x+3)}+\frac{x}{(x+6)(x-6)}\
&=\frac{(x+3)(x-6)+x(x+3)}{(x+6)(x+3)(x-6)}\
&=\frac{2x-6}{(x+6)(x+3)(x-6)}
\end{align*}Simplifying, we get $\dfrac{2x-6}{x^{2}-36}$. Therefore, the answer is D.

Perform the Operations and Simplify x+3x2+9x+18+xx2−36\frac { x + 3 } { x ^ { 2 } + 9 x + 18 } + \frac { x } { x ^ { 2 } - 36 }x2+9x+18x+3​+x2−36x​

Perform the Operations and Simplify $\frac { x + 3 } { x ^ { 2 } + 9 x + 18 } + \frac { x } { x ^ { 2 } - 36 }$