Solve for y xy=x+y

$x y = x + y$

Step 1

Subtract $y$ from both sides of the equation.

$x y - y = x$

Step 2

Factor $y$ out of $x y - y$ .

Factor $y$ out of $x y$ .

$y x - y = x$

Factor $y$ out of $- y$ .

$y x + y \cdot - 1 = x$

Factor $y$ out of $y x + y \cdot - 1$ .

$y (x - 1) = x$

Step 3

Divide each term in $y (x - 1) = x$ by $x - 1$ and simplify.

Divide each term in $y (x - 1) = x$ by $x - 1$ .

$\frac{y (x - 1)}{x - 1} = \frac{x}{x - 1}$

Simplify the left side.

Cancel the common factor of $x - 1$ .

Cancel the common factor.

$\frac{y (x - 1)}{x - 1} = \frac{x}{x - 1}$

Divide $y$ by $1$ .

$y = \frac{x}{x - 1}$