如果(2x+1)/(x-3)(x-4)=A/(3-x)+B/(x+4),那么3A+2B=?

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如果(2x+1)/(x-3)(x-4)=A/(3-x)+B/(x+4),那么3A+2B=?
如果(2x+1)/(x-3)(x-4)=A/(3-x)+B/(x+4),那么3A+2B=?

如果(2x+1)/(x-3)(x-4)=A/(3-x)+B/(x+4),那么3A+2B=?
-A /(x-3)+ B /(x-4) =[(B-A)x+4A-3B]/(X-3)(x-4)
由于(2x+1)/(x-3)(x-4)=A /(3-x)+ B /(x-4)
则 (B-A)x+4A-3B=2x+1
B-A=2
4A-3B=1
则:A=7 B=9
3A+2B=21+18=39

(2x+1)/(x-3)(x-4)
=A/(3-x)+B/(x+4)
=[A(x+4)+B(3-x)]/[(x-3)(x-4)]
=(A-B)x+(4A+3B)]/[(x-3)(x-4)]
比较系数得
A-B=2
4A+3B=1
解得B=-1,A=1
3A+2B=1

[2x+1)/(x-3)(x-4)=A/(3-x)+B/(x-4)=[(A-B)x+(-4A+3B)](/(x-3)(x-4),
A-B=2,4A-3B=-1
A=7,B=-9
3A+2B=3