已知m/n=5、,求（m/（m+n）)+(m/(m-n))-(n^2/(m^3-n^2))
问题描述：
已知m/n=5、,求（m/（m+n）)+(m/(m-n))-(n^2/(m^3-n^2))
答
题目是否应为 m / (m+n) + m / (m-n) - n^2 / (m^2-n^2) ?
m/n=5 m=5n
则原式 ＝m (m - n) / (m + n)*(m - n) + m (m + n) / (m - n)*(m + n) - n^2 / (m^2-n^2)
= (m^2 - mn) / (m^2-n^2) + (m^2 + mn) / (m^2-n^2) - n^2 / (m^2-n^2)
=(2m^2- n^2) / (m^2-n^2)
=[ 2(5n)^2 - n^2) ] / [ (5n)^2-n^2) ]
=49n^2 / 24n^2
=49/24
答
已知m=5n,则原式=(5n/(5n+n))+(5n/(5n-n))-(n^2)/(((5n)^3)-n^2)=(5/6)+(5/4)-[1/(125n-1)]=(25/12)-[1/(125n-1)]