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: Option 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)})