SOLUTION: Write the partial fraction decomposition of the rational expression. x-17/(x-2)(x-5) Do I just break this down? When I work it the answer I am getting is 5/(x-2)+-4/(x-5). B

Algebra ->  Rational-functions -> SOLUTION: Write the partial fraction decomposition of the rational expression. x-17/(x-2)(x-5) Do I just break this down? When I work it the answer I am getting is 5/(x-2)+-4/(x-5). B      Log On


   

Question 89890This question is from textbook Algegra & Trigonometry
: Write the partial fraction decomposition of the rational expression.
x-17/(x-2)(x-5)
Do I just break this down? When I work it the answer I am getting is 5/(x-2)+-4/(x-5). But I feel like I am missing something...
Thanks,
Annie C. This question is from textbook Algegra & Trigonometry

Found 2 solutions by funmath, stanbon:
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Hi Annie,
You got the right answer, I would write it like this though:
5%2F%28x-2%29-4%2F%28x-5%29
Happy Calculating!!!

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write the partial fraction decomposition of the rational expression.
x-17/(x-2)(x-5)
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Write (x-17)/(x-2)(x-5) = a/(x-2)+b/(x-5)
Reconfigure the right side as follows:
[(x-17)/(x-2)(x-5)] = [a(x-5)+b(x-2)]/[(x-2)(x-5)]
The numerators must be equal:
x-17 = (a+b)x+(-5a-2b)
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Equate the corresponding coefficients:
a+b = 1
-5a-2b=-17
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5a+5b=5
Add this to -5a-2b=-17 to get
3b=-12
b = -4
So, a=5
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Final Answer : (x-17)/(x-2)(x-5) = 5/(x-2)-4/(x-5)
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Cheers,
stan H.