Solve for x rx+h=sx-k

$r x + h = s x - k$

Step 1

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

$r x + h - s x = - k$

Step 2

Subtract $h$ from both sides of the equation.

$r x - s x = - k - h$

Step 3

Factor $x$ out of $r x - s x$ .

Factor $x$ out of $r x$ .

$x r - s x = - k - h$

Factor $x$ out of $- s x$ .

$x r + x (- s) = - k - h$

Factor $x$ out of $x r + x (- s)$ .

$x (r - s) = - k - h$

Step 4

Divide each term in $x (r - s) = - k - h$ by $r - s$ and simplify.

Divide each term in $x (r - s) = - k - h$ by $r - s$ .

$\frac{x (r - s)}{r - s} = \frac{- k}{r - s} + \frac{- h}{r - s}$

Simplify the left side.

Cancel the common factor of $r - s$ .

Cancel the common factor.

$\frac{x (r - s)}{r - s} = \frac{- k}{r - s} + \frac{- h}{r - s}$

Divide $x$ by $1$ .

$x = \frac{- k}{r - s} + \frac{- h}{r - s}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{k}{r - s} + \frac{- h}{r - s}$

Move the negative in front of the fraction.

$x = - \frac{k}{r - s} - \frac{h}{r - s}$

Simplify terms.

Combine the numerators over the common denominator.

$x = \frac{- k - h}{r - s}$

Factor $- 1$ out of $- k$ .

$x = \frac{- (k) - h}{r - s}$

Factor $- 1$ out of $- h$ .

$x = \frac{- (k) - (h)}{r - s}$

Factor $- 1$ out of $- (k) - (h)$ .

$x = \frac{- (k + h)}{r - s}$

Simplify the expression.

Rewrite $- (k + h)$ as $- 1 (k + h)$ .

$x = \frac{- 1 (k + h)}{r - s}$

Move the negative in front of the fraction.

$x = - \frac{k + h}{r - s}$