已知4x+8/(x-1)(x-5)=m/(x-5) + n/(x-1) ,则m、n的值是多少

题目

已知4x+8/(x-1)(x-5)=m/(x-5) + n/(x-1) ,则m、n的值是多少
答案是m=7,n=－3,

答案

4x+8/(x-1)(x-5)=m/(x-5) + n/(x-1)
[4x+8]/(x-1)(x-5)=[m(x-1)+n(x-5)]/(x-1)(x-5)
4x+8=m(x-1)+n(x-5)
=(m+n)x-m-5n
m+n=4
-m-5n=8
n=-3
m=7