Find the partial decomposition for the rational expression:

Question

15/(x^2-5x) is the rational expression. I got as far as 15/(x(x-5)). I don't know where to go from here.

Answer 1

You have done just half of the job: 15/(x^2-5x)  = 15/(x(x-5))

Next, assume that A/(x-5) + B/x = 15/(x(x-5))

Solving this for A and B will give you the final answer for this Fraction Decomposition problem:

15/(x^2-5x) = 3/(x-5) -3/x