已知：5x-4/(x-1)(2x-1)=A/x-1加上B/2x-1,则A,B的值?

题目

已知：5x-4/(x-1)(2x-1)=A/x-1加上B/2x-1,则A,B的值?

答案

A/x-1 + B/2x-1
=A(2x-1) +B(x-1)/(x-1)(2x-1)
=(2A+B)x-(A+B)/(x-1)(2x-1)
=5x-4/(x-1)(2x-1)
2A+B=5
A+B=4
解得 A=1 B=3