Perform the operations and simplify. $$\frac { x + 6 } { x ^ { 2 } + 13 x + 42 } + \frac { x } { x ^ { 2 } - 49 }$$
Assume that no denominators are 0 .
A) $\frac { 2 x - 49 } { x ^ { 2 } - 7 }$
B) $\frac { 2 x - 7 } { x ^ { 2 } - 49 }$
C) $\frac { 2 x - 7 } { x ^ { 2 } + 49 }$
D) $\frac { 2 x + 7 } { x ^ { 2 } - 49 }$

Question

Quizplus · Accepted Answer

First, factor the denominators: $x^2 + 13x + 42 = (x + 6)(x + 7)$ and $x^2 - 49 = (x + 7)(x - 7)$. To add the fractions, find a common denominator, which is $(x + 6)(x + 7)(x - 7)$. Simplify the numerators accordingly to get $\frac{2x - 7}{x^2 - 49}$.

Perform the Operations and Simplify x+6x2+13x+42+xx2−49\frac { x + 6 } { x ^ { 2 } + 13 x + 42 } + \frac { x } { x ^ { 2 } - 49 }x2+13x+42x+6​+x2−49x​

Perform the Operations and Simplify $\frac { x + 6 } { x ^ { 2 } + 13 x + 42 } + \frac { x } { x ^ { 2 } - 49 }$