Perform the indicated operation. Simplify, if possible. $\frac { 6 } { 4 x - 28 } + \frac { 4 } { 7 - x }$
A) $\frac { 11 } { 2 ( x - 7 ) }$
B) $\frac { 5 } { 2 ( x - 7 ) }$
C) $\frac { - 4 } { x - 7 }$
D) $\frac { - 5 } { 2 ( x - 7 ) }$

Question

Quizplus · Accepted Answer

First, simplify the denominators: $4x - 28$ can be simplified to $4(x - 7)$, and $7 - x$ can be rewritten as $-(x - 7)$ for consistency in terms of $x$. The given expression becomes $\frac{6}{4(x - 7)} + \frac{4}{-(x - 7)}$, which simplifies to $\frac{3}{2(x - 7)} - \frac{4}{x - 7}$. Finding a common denominator and combining the fractions gives $\frac{3 - 8}{2(x - 7)} = \frac{-5}{2(x - 7)}$, which matches option D.

Perform the Indicated Operation 64x−28+47−x\frac { 6 } { 4 x - 28 } + \frac { 4 } { 7 - x }4x−286​+7−x4​

Perform the Indicated Operation $\frac { 6 } { 4 x - 28 } + \frac { 4 } { 7 - x }$