The partial fractions can be found in a very easy way using the following method.

(3x-2)/(x-3)(x+1), the roots of the denominator are x = 3 and x = -1.

Representing as partial fractions we get the form A/(x - 3) + B(x + 1)

Let's find A, ignore the term (x - 3) and substitute the root x = 3 for all the other terms.

This gives us (3*3 - 2)/(3 + 1) = (9 - 2)/4 = 7/4

Similarly to find B, eliminate (x + 1) and substitute the root x = -1 in the other terms, we get (3*-1 - 2)/(-1 - 3) = 5/4

Therefore the partial fractions are (7/4)/(x - 3) + (5/4)/(x + 1)