若分式(4x+1)/(x-2)(x-5)恒等于分式A/(x-2)+B/(x-5),求A,B的值

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若分式(4x+1)/(x-2)(x-5)恒等于分式A/(x-2)+B/(x-5),求A,B的值

若分式(4x+1)/(x-2)(x-5)恒等于分式A/(x-2)+B/(x-5),求A,B的值
若分式(4x+1)/(x-2)(x-5)恒等于分式A/(x-2)+B/(x-5),求A,B的值

若分式(4x+1)/(x-2)(x-5)恒等于分式A/(x-2)+B/(x-5),求A,B的值
A/x-2+B/x-5
=(AX-5A+BX-2B)/(X-2)(X-5)
=[(A+B)X-(5A+2B)]/(X-2)(X-5)
而它又等于4X+1/(x-2)(x-5)
即 4=A+B
1=-(5A+2B)
解得:A=-3,B=7
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(4x+1)/(x-2)(x-5)恒等于分式A/(x-2)+B/(x-5)
两边同乘以x-2,令x=2,得
A=(9/(2-5))=-3
两边同乘以x-5,令x=5,得
B=(21/(5-2))=7