(4a-1)/[(a+2)(a-1)]=m/(a+2)+n/(a-1),求m,n的值

题目

(4a-1)/[(a+2)(a-1)]=m/(a+2)+n/(a-1),求m,n的值

答案

m/(a+2)+n/(a-1)=m*(a-1)+n*(a+2)/[(a+2)(a-1)]
4a-1=m*(a-1)+n*(a+2)/=(m+n)a+2n-m
于是 m+n=4 m=4-n
2n-m=-1 2n-4+n=-1 n=1
m=3