## 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 \[x=\frac{1}{2}\]

.