Question #N20
What is the simplified form of the expression $\frac{x^2 - 4}{x^2 + 4x + 4}$?
A. $\frac{x-2}{x+2}$
B. $\frac{x+2}{x-2}$
C. $\frac{x-2}{x+2}$
D. $\frac{x+2}{x+2}$
Correct Answer is: A
The expression can be simplified by factoring the numerator and the denominator. The numerator is a difference of squares, and the denominator is a perfect square trinomial. We have: \begin{align*} \frac{x^2 - 4}{x^2 + 4x + 4} &= \frac{(x+2)(x-2)}{(x+2)(x+2)}\\ &= \frac{x-2}{x+2}. \end{align*}