Solve for x y+x=ax

$y + x = a x$

Step 1

Subtract $a x$ from both sides of the equation.

$y + x - a x = 0$

Step 2

Subtract $y$ from both sides of the equation.

$x - a x = - y$

Step 3

Factor $x$ out of $x - a x$ .

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

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

Factor $x$ out of $- a x$ .

$x \cdot 1 + x (- a) = - y$

Factor $x$ out of $x \cdot 1 + x (- a)$ .

$x (1 - a) = - y$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $1 - a$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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