Question

已知m/n=5/3,求分式m/(m+n)+m/(m-n)-n^2/(m^2-n^2)的值

Answer 1

解：原式=（m²-mn＋m²＋mn）／（m-n）（m＋n）－n²／（m²－n²）
=（2m²－n²）／（m²－n²）
同时除以n²得
（2（m/n）²－1）／（（m/n）²－1）＝（2×（5/3）²-1）／（（5 /3）²-1）＝41/16

Answer 2

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