How can I solve this partial fraction #(7x-10)/(4x^2-12x+9)#?
1 Answer
Aug 1, 2018
Explanation:
Given:
#(7x-10)/(4x^2-12x+9)#
First note that:
#4x^2-12x+9 = (2x-3)^2#
is a perfect square trinomial.
So we are looking for a partial fraction expansion of the form:
#(7x-10)/(4x^2-12x+9) = A/(2x-3)+B/(2x-3)^2#
Mutiplying both sides by
#7x-10 = A(2x-3)+B#
Looking at the coefficient of
#A=7/2#
Putting
#B = 7(color(blue)(3/2))-10 = 1/2#
So:
#(7x-10)/(4x^2-12x+9) = 7/(2(2x-3))+1/(2(2x-3)^2)#