已知[-4x^m+2n y^3m-n]/(-2x^5m y2m+n)的商与-1/2x^3y^2是同类项,求m+n的值

题目

已知[-4x^m+2n y^3m-n]/(-2x^5m y2m+n)的商与-1/2x^3y^2是同类项,求m+n的值

答案

-1/2x^3y^2*(-2x^5m y2m+n)
=x^(5m+3)*y^(2m+n+2)与
-4x^m+2n y^3m-n
为同类项
则5m+3=m+2n,4m-2n+3=0
2m+n+2=3m-2,m-n-4=0
m=-11/2,n=-19/2
m+n=-15