#proofinatoot that there are infinitely many solutions to the equation \(xy = x + y\).

i.e. \[1 = \frac{1}{x} + \frac{1}{y}\]

Let \(x = c/a\) and \(y = c/b\). We have \(1 = \frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}\)

\(\iff c = a + b\).

So \(xy = x + y\) is satisfied when \(x = c/a\), \(y = c/b\) where \(c = a + b\), for any value of a and b.

e.g.: \(\frac{37}{15} + \frac{37}{22} = \frac{37}{15} \times \frac{37}{22} = \frac{1369}{330}\).