SOLUTION: Find the partial fraction decomposition of (26x^2+208x)/(x^2+1)(x+5)

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Question 242318: Find the partial fraction decomposition of
(26x^2+208x)/(x^2+1)(x+5)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

+26x%5E2%2B208x=A%28x%5E2%2B1%29%2BB%28x%2B5%29%2BCx%28x%2B5%29
+26x%5E2%2B208x=Ax%5E2%2BA%2BBx%2B5B%2BCx%5E2%2B5Cx
+26x%5E2%2B208x=%28A%2BC%29x%5E2%2B%28B%2B5C%29x%2B%285B%2BC%29
Comparing terms,
1)+A%2BC=26
2)+A%2B5B=0
3)+B%2B5C=208
From 1),
+A=26-C
Substitute into 2),
+26-C%2B5B=0
+5B-C=-26
+25B-5C=-130
Add this to 3)
+B%2B5C%2B25B-5C=-130%2B208
+26B=78
+B=3
Then,
+A%2B5B=0
+A=-5B=-15
and finally,
+A%2BC=26
+A=41