Perform the indicated operation. $\frac { 4 x + 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 x + 1 } { x ^ { 2 } + 6 x + 8 } + \frac { 6 } { x + 4 }$
A) $\frac { 14 x ^ { 2 } + 76 x + 73 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$
B) $\frac { 13 x ^ { 2 } + 76 x + 73 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$
C) $\frac { 13 x ^ { 2 } + 79 x + 73 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$
D) $\frac { 13 x ^ { 2 } + 76 x + 69 } { ( x + 2 ) ( x + 5 ) ( x + 4 ) }$

Question

Quizplus · Accepted Answer

First, factor the denominators: $x^2 + 7x + 10 = (x + 5)(x + 2)$ and $x^2 + 6x + 8 = (x + 4)(x + 2)$. The common denominator is $(x + 2)(x + 5)(x + 4)$. Adjust the numerators accordingly and sum them up to get $\frac{13x^2 + 76x + 73}{(x + 2)(x + 5)(x + 4)}$.

Perform the Indicated Operation 4x+2x2+7x+10+3x+1x2+6x+8+6x+4\frac { 4 x + 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 x + 1 } { x ^ { 2 } + 6 x + 8 } + \frac { 6 } { x + 4 }x2+7x+104x+2​+x2+6x+83x+1​+x+46​

Perform the Indicated Operation $\frac { 4 x + 2 } { x ^ { 2 } + 7 x + 10 } + \frac { 3 x + 1 } { x ^ { 2 } + 6 x + 8 } + \frac { 6 } { x + 4 }$