Simplify the expression. $\frac { - 1 } { x - 1 } - \frac { 4 } { ( x - 2 ) ^ { 2 } }$
A) $\frac { x ^ { 2 } - 18 } { ( 2 x - 3 ) ^ { 2 } }$
B) $\frac { - x ^ { 2 } - 7 } { ( x - 2 ) ^ { 2 } }$
C) $\frac { - x ^ { 2 } } { ( x - 1 ) ( x - 2 ) ^ { 2 } }$
D) $\frac { 10 x - 2 } { ( 2 x + 1 ) ^ { 2 } }$
E) $\frac { 2 x ^ { 2 } + 9 } { ( 2 x - 1 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

To simplify, find a common denominator and combine the two fractions. The common denominator is $(x-1)(x-2)^2$. Thus, after combining, we have $$\frac{-1(x-2)^2-4(x-1)}{(x-1)(x-2)^2}.$$ Simplifying the numerator gives $-(x^2-4x+3)$, which factors as $-(x-1)(x-3)$. Substituting this back in, the expression simplifies to $$\frac{-1(x-1)(x-3)}{(x-1)(x-2)^2}=\boxed{	extbf{(C)}\ \frac{-x^2}{(x-1)(x-2)^2}}.$$

Simplify the Expression −1x−1−4(x−2)2\frac { - 1 } { x - 1 } - \frac { 4 } { ( x - 2 ) ^ { 2 } }x−1−1​−(x−2)24​

Simplify the Expression $\frac { - 1 } { x - 1 } - \frac { 4 } { ( x - 2 ) ^ { 2 } }$