(6x+5)/(x2-x-12)=A/(x-4)+B/(X+3).则A+B=

问题描述:

(6x+5)/(x2-x-12)=A/(x-4)+B/(X+3).则A+B=

由题意:
A/(x-4)+B/(X+3).
=[A(x+3) +B(x-4)]/(x-4)(x+3)
=[(A+B)x+(3A-4B)]/(x^2-x-12)
=(6x+5)/(x2-x-12)
对照系数可以得出:
A+B=6
3A-4B=5
解得:A=29/7,B=13/7