Simplify \(\frac{x + 2}{x + 1}\) - \(\frac{x - 2}{x + 2}\)
A
\(\frac{3}{x + 1}\)
B
\(\frac{3x + 2}{(x + 1)(x + 2)}\)
C
\(\frac{5x + 6}{(x + 1)(x + 2)}\)
D
\(\frac{2x^2 + 5x + 2}{(x + 1)(x + 2)}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{x + 2}{x + 1}\) - \(\frac{x - 2}{x + 2}\) = \(\frac{(x + 2)(x + 2) - (x - 2)(x + 1)}{(x + 1)(x + 2)}\)
= \(\frac{(x^2 + 4x + 4) - (x^2 - x - 2)}{(x + 1)(x + 2)}\) = \(\frac{x^2 + 4x + 4 - x^2 + x + 2}{(x + 1)(x + 2)}\)
= \(\frac{5x + 6}{(x + 1)(x + 2)}\)
Source: Myschool Past Questions Archive (Record #31722)