Question

数学题，急需。各位帮帮忙。

1. 已知1/m+1/n=1/m+n ; 求:(1) n/m+m/n (2) m^2/n^2+n^2/m^2

2、化简求值：（x+2/x^2-2x - x-1/x^2-4x+4) ÷4-x/x 已知：x=3
阿，打错了，不是÷4-x/x 是x-4/x

Answer 1

1.(1)1/m + 1/n = 1/(m+n)
(n+m)/mn = 1/(m+n)
(n+m)^2 = mn
n^2 + m^2 = -mn
n/m + m/n =(n^2 + m^2)/mn =-mn/mn = -1
(2)m^2/n^2 + n^2/m^2 =(m^4 + n^4)/(nm)^2
= [(m^2 + n^2)^2 - 2(mn)^2]/(nm)^2
=[(mn)^2 - 2(mn)^2]/(nm)^2
=-(mn)^2/(mn)^2
=-1
2.(x+2/x^2-2x - x-1/x^2-4x+4) ÷4-x/x
=[(x+2)/x(x-2) - (x-1)/(x-2)^2]÷4-x/x
=[(x-4)/x(x-2)^2]×[x/(4-x)]
=-1/(x-2)^2
=-1/(3-2)^2
=-1

Answer 2

1.（1）n/m+n/m=2n/m

Answer 3

1/m+1/n=1/m+n
(m+n)/mn+1/(m+n)
m^2+n^2=-mn
n/m+m/n=(m^2+n^2)/mn=-1
m^2/n^2+n^2/m^2=(m/n+n/m)^2-2=-1
[(x+2)/x(x-2)-(x-1)/(x-2)^2]/[(x-4)/x]={1/(x-2)[(x-2)/x-(x-1)]}/[(x-4)/x]
={(x-4)/[x(x-2)^2]}/[(x-4)/x]=1/(x-2)^2=1

Answer 4

15