Solve for x y(x+a)=k(x+z)

$y (x + a) = k (x + z)$

Simplify $y (x + a)$ .

Start simplifying.

$0 + 0 + y (x + a) = k (x + z)$

Simplify by adding zeros.

$y (x + a) = k (x + z)$

Apply the distributive property.

$y x + y a = k (x + z)$

Apply the distributive property.

$y x + y a = k x + k z$

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

$y x + y a - k x = k z$

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

$y x - k x = k z - y a$

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

Factor $x$ out of $y x$ .

$x y - k x = k z - y a$

Factor $x$ out of $- k x$ .

$x y + x (- k) = k z - y a$

Factor $x$ out of $x y + x (- k)$ .

$x (y - k) = k z - y a$

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

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

$\frac{x (y - k)}{y - k} = \frac{k z}{y - k} + \frac{- y a}{y - k}$

Simplify the left side.

Cancel the common factor of $y - k$ .

Cancel the common factor.

$\frac{x (y - k)}{y - k} = \frac{k z}{y - k} + \frac{- y a}{y - k}$

Divide $x$ by $1$ .

$x = \frac{k z}{y - k} + \frac{- y a}{y - k}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{k z - y a}{y - k}$