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

题目

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

答案

-4x^(m+2)y^(3m-n)÷[-2x^(5m)y^(2m+n)]
=2x^(m+2-5m)y^(3m-n-2m-n)
=2x^(2-4m)y^(m-2n)
与-(1/2)x^3y^3是同类项
所以2-4m=3
4m=-1
m=-1/4
m-2n=3
n=-13/8
m+n
=-1/4-13/8
=-15/8