Question 558747
For {{{1/x}}}, {{{1/y}}}, and {{{1/z}}} to exist, the three denominators have to be different from zero, and so would be their product {{{xyz}}}
We can eliminate denominators by ultiplying both sides of the equation times  {{{xyz}}}
{{{xyz/x=xyz(1/y - 1/z)}}} --> {{{yz=xyz/y-xyz/z}}} --> {{{yz=xz-xy}}}
After getting rid of the denominators, we eant to get all the z's to one side of the equal sign.
{{{yz=xz-xy}}} --> {{{xz-yz-xy=0}}} --> {{{(x-y)z-xy=0}}} --> {{{(x-y)z=xy}}} --> {{{z=xy/(x-y)}}}