4x+1/(x-2)(x-5)=a/x-2+b/x-5

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4x+1/(x-2)(x-5)=a/x-2+b/x-5

4x+1/(x-2)(x-5)=a/x-2+b/x-5
4x+1/(x-2)(x-5)=a/x-2+b/x-5

4x+1/(x-2)(x-5)=a/x-2+b/x-5
由题意可得:
a/(x-2)+b/(x-5)
=[a(x-5)+b(x-2)]/[(x-2)*(x-5)]
=[(a+b)x-5a-2b]/[(x-2)*(x-5)]
=(4x+1)/[(x-2)(x-5)]
则有:
{ a+b=4 (1)
{ -5a-2b=1 (2)
(1)×2得:2a+2b=8 (3)
(2)+(3)得:-3a=9
解得:a=-3,b=7

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