Add or subtract.
-$\frac { 7 - x } { x - 4 } - \frac { 2 x - 4 } { 4 - x }$
A) $\frac { x + 11 } { x - 4 }$
B) $\frac { x + 3 } { x - 4 }$
C) $- \frac { x + 11 } { x - 4 }$
D) $- \frac { x + 3 } { x - 4 }$

Question

Quizplus · Accepted Answer

To subtract fractions, we need a common denominator. The common denominator for this problem is $(x-4)(4-x)$. Therefore, we have
$$\frac{7-x}{x-4}-\frac{2x-4}{4-x}=\frac{(7-x)(4-x)}{(x-4)(4-x)}-\frac{(2x-4)(x-4)}{(x-4)(4-x)}$$
Simplifying this expression yields
$$\frac{(7-x)(4-x)-(2x-4)(x-4)}{(x-4)(4-x)}=\frac{3x+12}{x-4}=\frac{3(x+4)}{x-4}$$
which is equivalent to choice B: $\frac{x+3}{x-4}$.

Add or Subtract 7−xx−4−2x−44−x\frac { 7 - x } { x - 4 } - \frac { 2 x - 4 } { 4 - x }x−47−x​−4−x2x−4​

Add or Subtract $\frac { 7 - x } { x - 4 } - \frac { 2 x - 4 } { 4 - x }$