Simplify the expression. $\frac { \frac { x } { x - 1 } + \frac { 1 } { x + 1 } } { \frac { 5 } { x - 1 } - \frac { 2 } { x + 1 } }$
A) $\frac { x ^ { 2 } + 2 x - 1 } { x - 1 }$
B) $\frac { 3 x + 7 } { x ^ { 2 } + 2 x - 1 }$
C) $\frac { 3 x + 7 } { x - 1 }$
D) $\frac { x ^ { 2 } - 2 x + 1 } { x - 1 }$
E) $\frac { x ^ { 2 } + 2 x - 1 } { 3 x + 7 }$

Question

Quizplus · Accepted Answer

To simplify the given expression, 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 $(x-1)(x+1)$, and the same applies for the terms in the denominator. Simplifying both parts gives $\frac{x(x+1)+1(x-1)}{(x-1)(x+1)}$ for the numerator and $\frac{5(x+1)-2(x-1)}{(x-1)(x+1)}$ for the denominator. Simplifying these expressions further gives $\frac{x^2+2x-1}{3x+7}$ after combining like terms and reducing, which matches choice E.

Simplify the Expression xx−1+1x+15x−1−2x+1\frac { \frac { x } { x - 1 } + \frac { 1 } { x + 1 } } { \frac { 5 } { x - 1 } - \frac { 2 } { x + 1 } }x−15​−x+12​x−1x​+x+11​​

Simplify the Expression $\frac { \frac { x } { x - 1 } + \frac { 1 } { x + 1 } } { \frac { 5 } { x - 1 } - \frac { 2 } { x + 1 } }$