若分式ax+1/(x-2)(x-5)恒等于A/x-2+b/x-5,求A.B的值

问题描述:

若分式ax+1/(x-2)(x-5)恒等于A/x-2+b/x-5,求A.B的值
ax+1/(x-2)(x-5)改为4x+1/(x-2)(x-5)

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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