Question

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

要有过程！

Answer 1

m/n=5/3
所以n/m=3/5

2m²/(m²-n²)
分子分母同除以m²
=2/(m²/m²-n²/m²)
=2/[1-(n/m)²]
=2/(1-9/25)
=25/8

n²/(n²-m²)
分子分母同除以n²
=1/(n²/n²-m²/n²)
=1/[1-(m/n)²]
=1/(1-25/9)
=-9/16

所以原式=25/8-9/16=41/16

Answer 2

(2m^2)/(m^2-n^2)+n^2/(n^2-m^2)

=(2m^2-n^2)/(m^2-n^2)

=m^2/(m^2-n^2)+1

=1/(1-(n/m)^2)+1

=1/(1-9/25)+1

=25/16+1

=41/16

Answer 3

数学中，可以直接这样求解的，令m=5，则n=3，代入式中，求得=41/16

Answer 4

=2/(1-n^2/m^2)+1/(1-m^2/n^2)
=2/(1-9/25)+1/(1-25/9)
=50/16-9/16
=41/16