(x-3)/(x-3x+2) = a/(x-1) - b/(x-2)
左边分母分解因式,右边通分得：
(x-3)/[(x-1)(x-2)] = [a(x-2)-b(x-1)]/[(x-1)(x-2)]
(x-3)/[(x-1)(x-2)] = [(a-b)x-(2a-b)]/[(x-1)(x-2)]
a-b=1,2a-b=3
a=2,b=1
ab=2*1=2