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)})
Correct Answer: Option C
Explanation
(frac{1}{x^2 + 5x + 6}) + (frac{1}{x^2 + 3x + 2}) = (frac{1}{(x + 1)(x + 2)}) + (frac{1}{(x + 1)(x + 1)})
(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)})