已知:(8x-9)/(x-2)(x+3)=A/(x+3)+B/(x-2),求A、B的值

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已知:(8x-9)/(x-2)(x+3)=A/(x+3)+B/(x-2),求A、B的值已知:(8x-9)/(x-2)(x+3)=A/(x+3)+B/(x-2),求A、B的值已知:(8x-9)/(x-2

已知:(8x-9)/(x-2)(x+3)=A/(x+3)+B/(x-2),求A、B的值
已知:(8x-9)/(x-2)(x+3)=A/(x+3)+B/(x-2),求A、B的值

已知:(8x-9)/(x-2)(x+3)=A/(x+3)+B/(x-2),求A、B的值
两边乘(x+3)(x-2)
8x-9=A(x-2)+B(x+3)
整理得8x-9=(A+B)x+(3B-2A)
所以
A+B=8
3B-2A=-9
所以A=33/5,B=7/5

两边乘以(x-2)(x+3)得
8x-9 =A(x-2) +B(x+3)
=(A+B)x+(3B-2A)
∴A+B=8
-2A+3B=-9
∴A=33/5
B=7/5

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