代数式的恒等变形3已知（x+y+-z）/z=(x-y+z)/y=(-x+y+z)/x且xyz不等于0求分式（x+y)(y+z）(z+x)/xyz的值
问题描述：
代数式的恒等变形3
已知（x+y+-z）/z=(x-y+z)/y=(-x+y+z)/x且xyz不等于0求分式（x+y)(y+z）(z+x)/xyz的值
答
依题意,
(x+y-z)/z=(x-y+z)/y
x^2y+xy^2-xyz=x^2z+xz^2-xyz
x(xy+y^2)=x(xz+z^2)
xy+y^2=xz+z^2
y^2-z^2=xz-xy
(y+z)(y-z)=x(z-y)
y+z=-x
x+y+z=0
原式={(-z)(-x)(-y)}/xyz=-xyz/xyz=-1