Perform the indicated operations. Simplify if possible.
-$\frac { 3 x } { x + 1 } + \frac { 4 } { x - 1 } - \frac { 6 } { x ^ { 2 } - 1 }$
A) $\frac { 3 x - 2 } { x - 1 }$
B) $\frac { x + 1 } { x - 1 }$
C) $\frac { 3 x - 2 } { x + 1 }$
D) $\frac { 3 x } { x - 1 }$

Question

Quizplus · Accepted Answer

First, recognize that $x^2 - 1$ is a difference of squares, so it factors into $(x + 1)(x - 1)$. This allows us to find a common denominator for all fractions: $(x + 1)(x - 1)$. Simplifying the expression with this common denominator and combining like terms leads to $\frac{3x(x - 1) + 4(x + 1) - 6}{(x + 1)(x - 1)}$, which simplifies further to $\frac{3x^2 - 3x + 4x + 4 - 6}{x^2 - 1}$, and then to $\frac{3x^2 + x - 2}{x^2 - 1}$. Factoring the numerator and simplifying the expression, we find that it simplifies to $\frac{3x - 2}{x - 1}$, which matches choice A.

Perform the Indicated Operations 3xx+1+4x−1−6x2−1\frac { 3 x } { x + 1 } + \frac { 4 } { x - 1 } - \frac { 6 } { x ^ { 2 } - 1 }x+13x​+x−14​−x2−16​

Perform the Indicated Operations $\frac { 3 x } { x + 1 } + \frac { 4 } { x - 1 } - \frac { 6 } { x ^ { 2 } - 1 }$