# How do you solve for x in xy = x + y?

Apr 7, 2015

color(red)(xy=x+y

Transposing $x$ to the Left Hand Side will give us

$x y - x = y$

$x \cdot \left(y - 1\right) = y$ ($x$ was a common factor on the Left Hand Side)

Dividing both sides by $\left(y - 1\right)$(Assuming y!=1), we get

color(green) (x = y/(y-1)