\[x+y=xy=\frac{x}{y}\]
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 \[x=\frac{1}{2}\]
.