# How do you write the partial fraction decomposition of the rational expression #(2x - 3) / (x - 1)^2 #?

##### 1 Answer

Jan 28, 2016

# 2/(x-1) -1/(x-1)^2#

#### Explanation:

Note that

# (x-1)^2 # has factors (x-1) and

# (x-1)^2 #

# rArr (2x-3)/(x-1)^2 = A/(x-1) + B/((x-1)^2# .................(*)Multiply both sides by

#(x-1)^2 # so 2x -3 = A(x-1) + B

To find A and B choose values for x and substitute into (*)

Note: choose x =1 and the term with A becomes 0.

x = 1 : substitute into )*) : -1 = 0 + B → B= - 1

Choose any value for x , say x = 0

x = 0 : substitute into (*) : - 3 = - A+B = -A - 1

so - A -1 = -3 → A = 2