Solve $x + y + z = xyz$ such that $x , y , z \neq0$ I came across the equation $x+y+z=xyz$ such that $x , y , z \neq 0$.
I set $x=1, y=2, z=3$ but how can i reach formal mathematical solution without " guessing " the answer ? Thank you

you can write $y+z=x(yz-1)$ and if $yz\ne1$ you will get $$x=\frac{y+z}{yz-1}$$
if $yz=1$ we get $y+z=0$ or $y^2+1=0$ which gives us complex solutions.
