若(5x-1)/(x+2)(2x-3)=M/(x+2)+N/(2x-3),求NM的值

题目

若(5x-1)/(x+2)(2x-3)=M/(x+2)+N/(2x-3),求NM的值

答案

M/(x+2)+N/(2x-3)
=[M(2X-3)+N(X+2)]/(x+2)(2x-3)
=[(2M+N)X+(2N-3M)]/(x+2)(2x-3)
∵(5x-1)/(x+2)(2x-3)=M/(x+2)+N/(2x-3),
∴2M+N=5
2N-3M=-1
解得M=11/7,N=13/7