Add, and then simplify, if possible. $\frac { 7 } { x + 2 } + \frac { 8 } { x - 4 }$
A) $\frac { 3 ( 5 x + 4 ) } { ( x + 2 ) ( x - 4 ) }$
B) $\frac { 2 } { ( x + 2 ) ( x - 4 ) }$
C) $\frac { 2 ( 5 x - 4 ) } { x + 2 }$
D) $\frac { ( 5 x - 4 ) } { ( x + 2 ) ( x - 4 ) }$
E) $\frac { 3 ( 5 x - 4 ) } { ( x + 2 ) ( x - 4 ) }$

Question

Quizplus · Accepted Answer

To add the fractions, find a common denominator: $(x + 2)(x - 4)$. The numerators become $7(x - 4) + 8(x + 2)$. Simplifying gives $7x - 28 + 8x + 16 = 15x - 12$. The simplified fraction is $\frac{15x - 12}{(x + 2)(x - 4)}$, which can be factored as $\frac{3(5x - 4)}{(x + 2)(x - 4)}$.

Add, and Then Simplify, If Possible 7x+2+8x−4\frac { 7 } { x + 2 } + \frac { 8 } { x - 4 }x+27​+x−48​

Add, and Then Simplify, If Possible $\frac { 7 } { x + 2 } + \frac { 8 } { x - 4 }$