已知(5x-4)/(x-5)(x+2)=A/(x-5)+B/(x+2) 求A和B的值

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已知(5x-4)/(x-5)(x+2)=A/(x-5)+B/(x+2) 求A和B的值
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已知(5x-4)/(x-5)(x+2)=A/(x-5)+B/(x+2) 求A和B的值
已知(5x-4)/(x-5)(x+2)=A/(x-5)+B/(x+2) 求A和B的值

已知(5x-4)/(x-5)(x+2)=A/(x-5)+B/(x+2) 求A和B的值
(5x-4)/(x-5)(x+2)=A/(x-5)+B/(x+2)
5x-4=A(x+2)+B(x-5)
5x-4=(A+B)x+(2A-5B)
∴﹛A+B=5
2A-5B=-4
∴A=3, B=2

两边乘以(x-5)(x+2)得
5x-4=A(x+2)+B(x-5)
=(A+B)x+(2A-5B)
∴A+B=5
2A-5B=-4
∴A=3
B=2