若x+y+z=0且xyz不等于0,求x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)的值

x+y+z=0
所以x+y=-z
x+z=-y
y+z=-x
x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)
=x/y+x/z+y/x+y/z+z/x+z/y
=(x+y)/z+(x+z)/y+(y+z)/x
=(-z/z)+(-y/y)+(-x/x)
=-1-1-1
=-3