1.x+y+z≠0且x/(y+z)=y/(x+y)=z/x+y,求x/(x+y+z)2.x+y+z=0,求证1/(x^2-y^2-z^2)+1/(y^2-z^2-x^2)+1/(z^2-x^2-y^2)=03.x^2-y^2=xy,求x^2y^-2+x^-2y^24.n/m中分子分母同时增加2，3…k（为正整数），m＞0，n＞0，情况如何5.建

Question

1.x+y+z≠0且x/(y+z) =y/(x+y) =z/x+y,求x/(x+y+z)
2.x+y+z=0,求证1/(x^2 -y^2 -z^2) +1/(y^2 -z^2-x^2)+1/(z^2-x^2-y^2) =0
3.x^2-y^2=xy,求x^2 y^-2 +x^-2 y^2
4.n/m中分子分母同时增加2，3…k（为正整数），m＞0，n＞0，情况如何
5.建筑学规定民用住宅窗户面积必须小于地板面积，但按采光标准，窗户面积与地板面积比应不小于10%，并且这个比值越大，住宅采光的条件越好。若同时增加相等的窗户面积和地板面积，住宅的采光条件是变好还是变坏？说明理由。

Answer 1

1.x/(y+z)=z/(x+y)
x(x+y)=z(y+z)
(x+y+z)(x-z)=0
x+y+z≠0得x=z
x/(y+z)=y/(x+y)
x/(y+z)=y/(z+y)
故y=z
因此x=y=z
x/(x+y+z)=1/3
2.x²-y²-z²=(x-y)(x+y)-z²=-(x-y)*z-z²=-(x-y+z)z=-(-2y)z=2yz
同理
y²-z²-x²=2zx
z²-x²-y²=2xy
1/(x²-y²-z²)+1/(y²-z²-x²)+1/(z²-x²-y²)
=1/2yz+1/2zx+1/2xy=(x+y+z)/2xyz
=0
3.x²-y²=xy得x²=y²+xy,y²=x²-xy
x²/y²+y²/x²=(y²+xy)/y²+(y²-xy)/x²=1+x/y+1-y/x=2+(x²-y²)/xy=2+1=3
4.(n+k)/(m+k)-n/m=(m-n)k/(m+k)m
若n>m则,n/m变小,若n