Perform the operations and simplify the result when possible. $\frac { 2 x } { x ^ { 2 } + 13 x + 22 } + \frac { 2 x } { x ^ { 2 } - 4 }$
A) $\begin{array} { r }
2 x - 9 \
\hline ( x + 11 ) ( x - 2 ) ( x + 2 )
\end{array}$
B) $\frac { 2 x ( 2 x + 9 ) } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$
C) $\frac { 2 x ( 2 x + 11 ) } { ( x + 9 ) ( x - 2 ) ( x + 2 ) }$
D) $\frac { 2 x + 9 } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$
E) $\frac { 2 x ( 2 x - 9 ) } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$

Question

Perform the operations and simplify the result when possible. $\frac { 2 x } { x ^ { 2 } + 13 x + 22 } + \frac { 2 x } { x ^ { 2 } - 4 }$
A) $\begin{array} { r } 
2 x - 9 \
\hline ( x + 11 ) ( x - 2 ) ( x + 2 )
\end{array}$
B) $\frac { 2 x ( 2 x + 9 ) } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$
C) $\frac { 2 x ( 2 x + 11 ) } { ( x + 9 ) ( x - 2 ) ( x + 2 ) }$
D) $\frac { 2 x + 9 } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$
E) $\frac { 2 x ( 2 x - 9 ) } { ( x + 11 ) ( x - 2 ) ( x + 2 ) }$

Quizplus · Accepted Answer

First, factor the denominators: $x^2 + 13x + 22 = (x + 11)(x + 2)$ and $x^2 - 4 = (x - 2)(x + 2)$. To add the fractions, find a common denominator, which is $(x + 11)(x - 2)(x + 2)$. Adjust the numerators accordingly and simplify to get $\frac{2x(2x + 9)}{(x + 11)(x - 2)(x + 2)}$.

Perform the Operations and Simplify the Result When Possible 2xx2+13x+22+2xx2−4\frac { 2 x } { x ^ { 2 } + 13 x + 22 } + \frac { 2 x } { x ^ { 2 } - 4 }x2+13x+222x​+x2−42x​

Perform the Operations and Simplify the Result When Possible $\frac { 2 x } { x ^ { 2 } + 13 x + 22 } + \frac { 2 x } { x ^ { 2 } - 4 }$