Question

已知m/n=5/3,求(m/m+n)+(m/m-n)-n*n/(m+n)(m-n)的值

Answer 1

m/(m+n)+m/(m-n)-n^2/(m^2-n^2)
=m(m-n)/(m+n)(m-n)+m(m+n)/(m-n)(m+n)-n^2/(m^2-n^2)
=（m(m-n)+m(m+n)）/(m^2-n^2)-n^2/(m^2-n^2)
=（2m^2)）/(m^2-n^2)-n^2/(m^2-n^2)
=(2m^2-n^2)/(m^2-n^2)
m/n=5/3
m=5n/3带入
=(2（5n/3）^2-n^2)/(（5n/3）^2-n^2)
=（2（5n/3）^2-n^2)/(（5n/3）^2-n^2)
=(41n^2/9)/(16N^2/9)
=41/16

Answer 2

通分得（2m^2-n^2）／（（m+n）*（m-n）） 然后上下同时除以n^2.就可以得到由m／n和常数构成的式子.带入m／n的值即可. 答案是41/16

Answer 3

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