Question 89890
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.