Question #N999
If $x$ is a positive integer, what is the smallest possible value of $x$ such that $\frac{x^2 - 4}{x - 2}$ is an integer?
A. 1
B. 2
C. 3
D. 4
Correct Answer is: D
The expression $\frac{x^2 - 4}{x - 2}$ can be simplified by factoring the numerator: $\frac{x^2 - 4}{x - 2} = \frac{(x+2)(x-2)}{x - 2} = x + 2$, as long as $x \neq 2$. Since $x$ is a positive integer, the smallest possible value of $x$ that makes this expression an integer is $x = 4$.