已知A/(x-5)+B/(x+2)=(5x-4)/(x*x-3x-10)其中A,B为常数,试求A,B的值

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已知A/(x-5)+B/(x+2)=(5x-4)/(x*x-3x-10)其中A,B为常数,试求A,B的值
已知A/(x-5)+B/(x+2)=(5x-4)/(x*x-3x-10)其中A,B为常数,试求A,B的值

已知A/(x-5)+B/(x+2)=(5x-4)/(x*x-3x-10)其中A,B为常数,试求A,B的值
A/(x-5)+B/(x+2)=A(x+2)+B(x-5)/(x*x-3x-10)=(5x-4)/(x*x-3x-10)
所以A+B = 5
2A-5B = -4
所以B = 2,A = 3

A/(x-5)+B/(x+2)
= [A(x+2)+B(x-5)]/(x*x-3x-10)
= [(A+B)x+(2A-5B)]/(x*x-3x-10)
(A+B)x+(2A-5B)=5x-4
A+B=5
2A-5B=-4
A=3
B=2