Question #N103
What is the value of $\frac{x^2 + 2x + 1}{x^2 - 1}$ when $x=3$?
A. 2
B. 4
C. 8
D. 16
Correct Answer is: A
We can simplify the expression first by factoring the numerator and denominator: $\frac{x^2 + 2x + 1}{x^2 - 1} = \frac{(x+1)(x+1)}{(x+1)(x-1)}$. Since $x=3$, we can substitute to get $\frac{(3+1)(3+1)}{(3+1)(3-1)} = \frac{(4)(4)}{(4)(2)} = \frac{16}{8} = 2$.