Simplify.
-$$\frac { \frac { 7 } { x - 6 } - \frac { 4 } { 6 - x } } { \frac { 4 } { x - 6 } - \frac { 4 } { x } }$$
A) $\frac { 7 x } { 6 }$
B) $\frac { - 11 x ^ { 2 } + 66 x } { - 24 x + 144 }$
C) $\frac { 3 x } { 24 }$
D) $\frac { 11 \mathrm { x } } { 24 }$

Question

Quizplus · Accepted Answer

First, notice that $\frac{4}{6-x}$ can be rewritten as $-\frac{4}{x-6}$ by factoring out a negative from the denominator. This simplifies the numerator to $\frac{7}{x-6} + \frac{4}{x-6}$ which simplifies further to $\frac{11}{x-6}$. The denominator simplifies to $\frac{4}{x-6} - \frac{4}{x}$, which can be combined into a single fraction with a common denominator, resulting in $\frac{4x - 4(x-6)}{x(x-6)}$, simplifying to $\frac{24}{x(x-6)}$. The overall expression simplifies to $\frac{11x}{24}$, making choice D correct.

Simplify - 7x−6−46−x4x−6−4x\frac { \frac { 7 } { x - 6 } - \frac { 4 } { 6 - x } } { \frac { 4 } { x - 6 } - \frac { 4 } { x } }x−64​−x4​x−67​−6−x4​​

Simplify
- $\frac { \frac { 7 } { x - 6 } - \frac { 4 } { 6 - x } } { \frac { 4 } { x - 6 } - \frac { 4 } { x } }$