Add or subtract as indicated and simplify if possible.
-$$\frac { x } { x + 2 } - \frac { 3 - x ^ { 2 } } { x ^ { 2 } - 4 }$$
A) $\frac { x ^ { 3 } + 2 x - 3 } { \left( x ^ { 2 } - 4 \right) ( x + 2 ) }$
B) $\frac { - 2 x - 3 } { x ^ { 2 } - 4 }$
C) $\frac { 2 x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 4 }$
D) $\frac { x ^ { 2 } + x - 3 } { - x ^ { 2 } + x + 6 }$

Question

Quizplus · Accepted Answer

To simplify the given expression, first notice that $x^2 - 4$ can be factored into $(x + 2)(x - 2)$. This means the common denominator for both fractions is $x^2 - 4$, or equivalently, $(x + 2)(x - 2)$. The first fraction is already over $x + 2$, so it needs to be multiplied by $(x - 2)/(x - 2)$ to have the same denominator as the second fraction. This gives:$$\frac{x(x - 2)}{x^2 - 4} - \frac{3 - x^2}{x^2 - 4}$$Simplifying the numerator:$$= \frac{x^2 - 2x - 3 + x^2}{x^2 - 4}$$$$= \frac{2x^2 - 2x - 3}{x^2 - 4}$$This matches choice (C).

Add or Subtract as Indicated and Simplify If Possible xx+2−3−x2x2−4\frac { x } { x + 2 } - \frac { 3 - x ^ { 2 } } { x ^ { 2 } - 4 }x+2x​−x2−43−x2​

Add or Subtract as Indicated and Simplify If Possible $\frac { x } { x + 2 } - \frac { 3 - x ^ { 2 } } { x ^ { 2 } - 4 }$