SOLUTION: Write the partial fraction decomposition of the rational expression. x-6 ___________ (x-2)(x-3)

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Question 327895: Write the partial fraction decomposition of the rational expression.

x-6
___________
(x-2)(x-3)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-6%29%2F%28%28x-2%29%28x-3%29%29=A%2F%28x-2%29%2BB%2F%28x-3%29
Multiply both sides by %28x-2%29%28x-3%29
x-6=A%28x-3%29%2BB%28x-2%29
x-6=Ax%2BBx-3A-2B
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.
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1.A%2BB=1
2.3A%2B2B=6
Multiply eq.1 by -3 and add the equations together to eliminate A.
-3A-3B%2B3A%2B2B=-3%2B6
-B=3
highlight%28B=-3%29
Then use either equation to solve for A.
A-3=1
highlight%28A=4%29
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%28x-6%29%2F%28%28x-2%29%28x-3%29%29=4%2F%28x-2%29-3%2F%28x-3%29