Question

Write the partial fraction decomposition of the rational expression.
(80-14x)/(x^3 -8x^2 +16x)

Answer 1

(80-14x)/(x^3 -8x^2 +16x)
=(80-14x)/(x(x-4)²)
=A/x + B/(x-4) + C/(x-4)²

=>
A(x-4)²+Bx(x-4)+Cx = 80-14x
=>
x²(A+B) + (C-4B-8A)x + 16A = 80-14x
=>
A=5
B=-5
C=6
Can you take it from here?

Answer 2

I got it; thank you so much!

Answer 3

You're welcome!