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