## Solving a Three Sided Equation

Suppose we have the equation.
$x+y=xy=\frac{x}{y}$

We can solve this by writing as simultaneous equations.
$x+y=xy$
(1)
$xy=\frac{x}{y}$

Multiplying both sides of (2) by
$y$
then dividing by
$x$
gives
$y^2=1 \rightarrow y= \pm 1$
.
Then (1) becomes
$x+1=x$
- using
$y=1$
- which has no solution, or
$x-1=-x$
which has the solution
$x=\frac{1}{2}$
.