Resolve 3x2+x−2 3 x 2 + x − 2 into partial fractions

Resolve $\frac{3}{x^2+x-2}$ into partial fractions

Answer Details

$\frac{3}{x^2+x-2}$ = $\frac{3}{(x-1)(x+1)}$
$\frac{A}{x-1}$ + $\frac{B}{x+2}$
A(x + 2) + B(x - 1) = 3
when x = 1, 3A = 3 $\to$ a = 1
when x = -2, -3B = 3 $\to$ B = -1
3 = 1 - 1
= $\frac{1}{x-1}+\frac{1}{x+2}$