Add or subtract.
-$\frac { 1 } { ( x - 3 ) ( x + 3 ) } - \frac { 3 } { ( x + 3 ) ( x - 1 ) }$
A) $\frac { - 2 ( x - 4 ) } { ( x - 3 ) ( x + 3 ) ( x - 1 ) }$
B) $\frac { 2 ( 2 x - 5 ) } { ( x - 3 ) ( x + 3 ) ( x - 1 ) }$
C) $\frac { 2 ( x - 4 ) } { ( x - 3 ) ( x + 3 ) ( x - 1 ) }$
D) $\frac { - 2 ( x - 2 ) } { ( x - 3 ) ( x + 3 ) ( x - 1 ) }$

Question

Quizplus · Accepted Answer

To add or subtract fractions, you need a common denominator. The least common denominator (LCD) here is $(x - 3)(x + 3)(x - 1)$. Converting each fraction to have this LCD and then subtracting gives: $\frac{1(x - 1) - 3(x - 3)}{(x - 3)(x + 3)(x - 1)} = \frac{x - 1 - 3x + 9}{(x - 3)(x + 3)(x - 1)} = \frac{-2x + 8}{(x - 3)(x + 3)(x - 1)} = \frac{-2(x - 4)}{(x - 3)(x + 3)(x - 1)}$.

Add or Subtract 1(x−3)(x+3)−3(x+3)(x−1)\frac { 1 } { ( x - 3 ) ( x + 3 ) } - \frac { 3 } { ( x + 3 ) ( x - 1 ) }(x−3)(x+3)1​−(x+3)(x−1)3​

Add or Subtract $\frac { 1 } { ( x - 3 ) ( x + 3 ) } - \frac { 3 } { ( x + 3 ) ( x - 1 ) }$