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

Let $x = 1$, then $yz = y+z$.
Let $y = z$, then $y\cdot y = y^2 = 2y$.
$\frac{y^2}y = y = 2$.
Using substitution of $x=1$, $y=2$:
$1 + 2 + z = 2z$
$1 + 2 = 2z-z$
$z=3$
$1\times2\times3 = 1 + 2 + 3$
If $x = y = z$, $x$ to $z$ would equal $3^{\frac12}$ .
