Solve for y xy=x-y

$x y = x - y$

Step 1

Add $y$ to both sides of the equation.

$x y + y = x$

Step 2

Factor $y$ out of $x y + y$ .

Factor $y$ out of $x y$ .

$y x + y = x$

Raise $y$ to the power of $1$ .

$y x + y = x$

Factor $y$ out of $y^{1}$ .

$y x + y \cdot 1 = x$

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 $1$ .

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