已知3m=2n,则m/(m+n)+n/(m-n)-n^2/(m^2-n^2)=?

题目

已知3m=2n,则m/(m+n)+n/(m-n)-n^2/(m^2-n^2)=?

答案

m/(m+n)+n/(m-n)-n^2 /(m^2-n^2)
=[m(m-n)+n(m+n)-n^2]/(m^2-n^2)
=m^2/(m^2-n^2)
=1/(1-(n/m)^2)
=1/(1-(3/2)^2)
=4/(4-9)
=-4/5