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)(x+z)(y+z)]/xyz的值.

题目

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)(x+z)(y+z)]/xyz的值.

答案

(x+y-z)/z=(y+z-x)/x=(z+x-y)/y [x+y]/z-1=[y+z]/x-1=[z+x]/y-1 [x+y]/z=[y+z]/x=[z+x]/y 设[x+y]/z=[y+z]/x=[z+x]/y=k k[x+y+z]=[(y+z)/x]*x+[(z+x)/y]*y+[(x+y/z]*z=2[x+y+z] k=2 (x+y)(y+z)(z+x)/xyz =(x+y)/z*(y...