Subtract. Simplify, if possible.
-$$\frac { 7 } { 2 x - 3 } - \frac { 5 } { 3 - 2 x }$$
A) $\frac { - 12 } { 2 x - 3 }$
B) $\frac { - 2 } { 2 x - 3 }$
C) $\frac { 12 } { 2 x - 3 }$
D) $\frac { 2 } { 2 x - 3 }$

Question

Quizplus · Accepted Answer

The correct answer is C.To subtract the fractions, we need to find a common denominator. The common denominator of $2x-3$ and $3-2x$ is $(2x-3)(3-2x)$. So, we can rewrite the expression as:$$\frac { 7 } { 2 x - 3 } - \frac { 5 } { 3 - 2 x } = \frac { 7(3-2x) } { (2x-3)(3-2x) } - \frac { 5(2x-3) } { (2x-3)(3-2x) }$$Now, we can combine the numerators and simplify:$$\frac { 7(3-2x) } { (2x-3)(3-2x) } - \frac { 5(2x-3) } { (2x-3)(3-2x) } = \frac { 21-14x - 10x + 15 } { (2x-3)(3-2x) }$$$$\frac { 21-14x - 10x + 15 } { (2x-3)(3-2x) } = \frac { 36 - 24x } { (2x-3)(3-2x) }$$$$\frac { 36 - 24x } { (2x-3)(3-2x) } = \frac { 12(3-2x) } { (2x-3)(3-2x) }$$$$\frac { 12(3-2x) } { (2x-3)(3-2x) } = \frac { 12 } { 2x-3 }$$Therefore, the answer is C.

Subtract Simplify, If Possible 72x−3−53−2x\frac { 7 } { 2 x - 3 } - \frac { 5 } { 3 - 2 x }2x−37​−3−2x5​

Subtract Simplify, If Possible $\frac { 7 } { 2 x - 3 } - \frac { 5 } { 3 - 2 x }$