Question

Integrate -> (x-9)/[(x+5)(x-6)]
I'm sure it's partial fraction decomp, which If I can just get started I can easily finish! any help is appreciated. (I don't want the answer!)

Answer 1

Baldwin u here

Answer 2

yes

Answer 3

\[\frac{x-9}{(x+5)(x-6)}= \frac{A}{x+5}+\frac{B}{x-6}=\frac{Ax-6A+Bx+5B}{(x+5)(x-6)}\]
collect terms in the numerator, and set corresponding terms equal
(A+B) x + (5B-6A) = x - 9
so the coefficient of x must be equal: (A+B) = 1
and the constant term must be equal: (5B-6A) = -9

Answer 4

Sorry Baldwin My net is creating issues.....am working on your question...apologies for the delay

Answer 5

Ah! thanks for reply, I'll award medal once I finish

Answer 6

My only issue is now that A+B =1 could make A or B a lot of things, I think I'm supposed to set the terms equal to another to cancel, but in this example that itsn't the case

Answer 7

okay sorry was in class, but I got A=14/11 and B=-3/11 so its simple \[(14/11) \int\limits_{}^{} 1/(x+5) + (-3/11) \int\limits_{}^{} 1/(x-6)\]

Answer 8

(14/11) ln (|x+5|) + (-3/11) ln (|x-6|) + C