Resolve (frac{3}{x^2 + x – 2}) into partial fractions
-
A.
(frac{1}{x – 1} – frac{1}{x + 2}) -
B.
(frac{1}{x + 1} + frac{1}{x – 2}) -
C.
(frac{1}{x + 1} – frac{1}{x – 2}) -
D.
(frac{1}{x – 2} + frac{1}{x + 2})
Correct Answer: Option A
Explanation
(frac{3}{x^2 + x – 2}) = (frac{3}{(x – 1)(x + 2)})
(frac{A}{x – 1}) + (frac{B}{x + 2})
A(x + 2) + B(x – 1) = 3
when x = 1, 3A = 3 (to) a = 1
when x = -2, -3B = 3 (to) B = -1
= (frac{1}{x – 1} – frac{1}{x + 2})