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 is A

\(\frac{3}{x^2 + x - 2}\) = \(\frac{3}{(x - 1)(x + 2)}\)

\(\frac{A}{x - 1}\) + \(\frac{B}{x + 2}\)

A(x + 2) + B(x - 1) = 3

when x = 1, 3A = 3 \(\to\) a = 1

when x = -2, -3B = 3 \(\to\) B = -1

= \(\frac{1}{x - 1} - \frac{1}{x + 2}\)