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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  
\[x=\frac{1}{2}\]
.

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