Simplify the following complex fraction. $\frac { \frac { 1 } { x + 7 } - \frac { 8 } { x - 9 } } { \frac { x } { x - 9 } + \frac { 5 } { x + 7 } }$
A) $\frac { - 7 x - 65 } { x ^ { 2 } + 12 x - 45 }$
B) $\frac { - 7 } { x + 5 }$
C) $\frac { x - 17 } { x ^ { 2 } + 7 x + 5 }$
D) $\frac { - 7 x + 47 } { x ^ { 2 } + 12 }$
E) $\frac { x - 2 } { x ^ { 2 } - 2 x - 63 }$

Question

Quizplus · Accepted Answer

To simplify the given complex fraction, we first find a common denominator for both the numerator and the denominator of the complex fraction. The common denominator for the terms in the numerator is $(x+7)(x-9)$, and for the terms in the denominator, it is also $(x+7)(x-9)$. Simplifying both parts and then dividing the simplified numerator by the simplified denominator gives $\frac{-7x-65}{x^2+12x-63}$, which matches choice A after further simplification.

Simplify the Following Complex Fraction 1x+7−8x−9xx−9+5x+7\frac { \frac { 1 } { x + 7 } - \frac { 8 } { x - 9 } } { \frac { x } { x - 9 } + \frac { 5 } { x + 7 } }x−9x​+x+75​x+71​−x−98​​

Simplify the Following Complex Fraction $\frac { \frac { 1 } { x + 7 } - \frac { 8 } { x - 9 } } { \frac { x } { x - 9 } + \frac { 5 } { x + 7 } }$