SOLUTION: Write the partial fraction decomposition of the rational expression X+1/(x-2)^2(x+4)

Algebra ->  Rational-functions -> SOLUTION: Write the partial fraction decomposition of the rational expression X+1/(x-2)^2(x+4)      Log On


   

Question 935798: Write the partial fraction decomposition of the rational expression
X+1/(x-2)^2(x+4)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

x%2B1=A%28x-2%29%28x%2B4%29%2BB%28x%2B4%29%2BC%28x-2%29%5E2
x%2B1=A%28x%5E2%2B2x-8%29%2BB%28x%2B4%29%2BC%28x%5E2-4x%2B4%29
x%2B1=%28A%2BC%29x%5E2%2B%282A%2BB-4C%29x%2B%28-8A%2B4B%2B4C%29
So then,
A%2BC=0
A=-C
.
.
2A%2BB-4C=1
2%28-C%29%2BB-4C=1
1.B-6C=1
.
.
-8A%2B4B%2B4C=1
-8%28-C%29%2B4B%2B4C=1
2.4B%2B12C=1
Multiply eq. 1 by 2 and add to eq. 2,
2B-12C%2B4B%2B12C=2%2B1
6B=3
B=1%2F2
Then,
1%2F2-6C=1
-6C=1%2F2
C=-1%2F12
A=1%2F12
So then,