SOLUTION: write the partial fraction decomposition of the given rational expression _____2___ 2x^2-11x+5

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Question 1008911: write the partial fraction decomposition of the given rational expression

_____2___
2x^2-11x+5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%282x%5E2-11x%2B5%29=2%2F%28%282x-1%29%28x-5%29%29=A%2F%282x-1%29%2BB%2F%28x-5%29
leads to,
2=A%28x-5%29%2BB%282x-1%29
2=%28A%2B2B%29x%2B%28-5A-B%29
So then,
1.A%2B2B=0 <-- x coefficient
2.-5A-B=2 <-- constant coefficient
From eq. 1,
A=-2B
Substituting into eq. 2,
-5%28-2B%29-B=2
10B-B=2
9B=2
B=2%2F9
So,
A=-4%2F9
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highlight%282%2F%282x%5E2-11x%2B5%29=-4%2F%289%282x-1%29%29%2B2%2F%289%28x-5%29%29%29