Express (frac{2}{x + 3} – frac{1}{x – 2}) as a simple fraction
-
A.
(frac{x – 7}{x^2 + x – 6}) -
B.
(frac{x – 1}{x^2 + x – 6}) -
C.
(frac{x – 2}{x^2 + x – 6}) -
D.
(frac{x – 27}{x^2 + x – 6})
Correct Answer: Option A
Explanation
(frac{2}{x + 3} – frac{1}{x – 2}) = (frac{2(x – 2) – (x – 3)}{(x + 3) (x – 2)})
= (frac{2x – 4 – x – 3}{x^2 – 2x + 3x – 6})
= (frac{x -7}{x^2 + x – 6})
= (frac{x – 7}{x^2 + x – 6})