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. \(\frac{2x^2 + 5x + 2}{(x + 1)(x + 2)}\)
Correct Answer: C
Explanation
\(\frac{x + 2}{x + 1}\) - \(\frac{x - 2}{x + 2}\) = \(\frac{(x + 2)(x + 2) - (x -2) - (x - 2)(x + 1)}{(x + 1)(x + 2)}\)
= \(\frac{(x^2 + 4x + 4) - (x^2 - x - 2)}{(x + 1)(x + 2)}\) = \(\frac{x^2 + 4x + 4 - x^2 + x + 2}{(x + 1)(x + 2)}\)
= \(\frac{5x + 6}{(x + 1)(x + 2)}\)
