Simplify \(\frac{1}{x^2 + 5x + 6}\) + \(\frac{1}{x^2 + 3x + 2}\)
A
\(\frac{x}{(x +2)(x - 3)}\)
B
\(\frac{2}{(x + 5)(x - 3)}\)
C
\(\frac{2}{(x + 1)(x + 3)}\)
D
\(\frac{2}{(x - 1)(x - 3)}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{1}{x^2 + 5x + 6}\) + \(\frac{1}{x^2 + 3x + 2}\) = \(\frac{1}{(x + 2)(x + 3)}\) + \(\frac{1}{(x + 1)(x + 2)}\)
\(\frac{(x + 1)+ (x + 3)}{(x + 1)(x + 2)(x + 3)}\) = \(\frac{x + 1 + x + 3}{(x + 1)(x + 2)(x + 3)}\)
\(\frac{2x + 4}{(x + 1)(x + 2)(x + 3)}\) = \(\frac{2(x + 2)}{(x + 1)(x + 2)(x + 3)}\)
= \(\frac{2}{(x + 1)(x + 3)}\)
Source: Myschool Past Questions Archive (Record #31731)