Perform the indicated operation. $\frac { x } { x ^ { 2 } - 4 } + \frac { 6 } { x - 2 }$
A) $\frac { 7 x - 6 } { ( x + 2 ) ( x - 2 ) }$
B) $\frac { 7 x - 12 } { x - 2 }$
C) $\frac { 7 x - 12 } { x + 2 }$
D) $\frac { 7 x + 12 } { ( x + 2 ) ( x - 2 ) }$

Question

Quizplus · Accepted Answer

To add two fractions with different denominators, we need to first find the LCD. Here, the denominators are $x^2-4$ and $x-2$. The first denominator can be factored as $(x+2)(x-2)$. The LCD is therefore $(x+2)(x-2)$. We can rewrite the given expression using the common denominator: $$\frac{x}{x^2-4}+\frac{6}{x-2}=\frac{x}{(x+2)(x-2)}+\frac{6}{x-2}.$$ To add these fractions, we need to have the same denominator: $$\frac{x}{(x+2)(x-2)}+\frac{6}{x-2}=\frac{x}{(x+2)(x-2)}+\frac{6(x+2)}{(x+2)(x-2)}.$$ Combining the fractions gives $$\frac{x}{(x+2)(x-2)}+\frac{6(x+2)}{(x+2)(x-2)}=\frac{7x+12}{(x+2)(x-2)}.$$ Therefore, the answer is (D).

Perform the Indicated Operation xx2−4+6x−2\frac { x } { x ^ { 2 } - 4 } + \frac { 6 } { x - 2 }x2−4x​+x−26​

Perform the Indicated Operation $\frac { x } { x ^ { 2 } - 4 } + \frac { 6 } { x - 2 }$