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)

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)
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)

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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(4x+1)/[(x-2)(x-5)]恒等于a/(x-2)+b/(x-5)
(4x+1)/[(x-2)(x-5)]恒等于[a(x-5)+b(x-2)]/[(x-2)(x-5)]
(4x+1)/[(x-2)(x-5)]恒等于[(a+b)x-5a-2b]/[(x-2)(x-5)]
∴4x+1恒等于(a+b)x-5a-b
恒等需同类项系数相等
∴4=a+b且 -5a-b=1
∴b=7,a=-3