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

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/08 21:28:07

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

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

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