Solve for x H/(M(x-y))=S

$\frac{H}{M (x - y)} = S$

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$M (x - y), 1$

The LCM of one and any expression is the expression.

$M (x - y)$

Step 2

Multiply each term in $\frac{H}{M (x - y)} = S$ by $M (x - y)$ to eliminate the fractions.

Multiply each term in $\frac{H}{M (x - y)} = S$ by $M (x - y)$ .

$\frac{H}{M (x - y)} (M (x - y)) = S (M (x - y))$

Simplify the left side.

Cancel the common factor of $M (x - y)$ .

Cancel the common factor.

$\frac{H}{M (x - y)} (M (x - y)) = S (M (x - y))$

Rewrite the expression.

$H = S (M (x - y))$

Simplify the right side.

Apply the distributive property.

$H = S (M x + M (- y))$

Rewrite using the commutative property of multiplication.

$H = S (M x - M y)$

Apply the distributive property.

$H = S (M x) + S (- M y)$

Rewrite using the commutative property of multiplication.

$H = S M x - S M y$

Step 3

Solve the equation.

Rewrite the equation as $S M x - S M y = H$ .

$S M x - S M y = H$

Add $S M y$ to both sides of the equation.

$S M x = H + S M y$

Divide each term in $S M x = H + S M y$ by $S M$ and simplify.

Divide each term in $S M x = H + S M y$ by $S M$ .

$\frac{S M x}{S M} = \frac{H}{S M} + \frac{S M y}{S M}$

Simplify the left side.

Cancel the common factor of $S$ .

Cancel the common factor.

$\frac{S M x}{S M} = \frac{H}{S M} + \frac{S M y}{S M}$

Rewrite the expression.

$\frac{M x}{M} = \frac{H}{S M} + \frac{S M y}{S M}$

Cancel the common factor of $M$ .

Cancel the common factor.

$\frac{M x}{M} = \frac{H}{S M} + \frac{S M y}{S M}$

Divide $x$ by $1$ .

$x = \frac{H}{S M} + \frac{S M y}{S M}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $S$ .

Cancel the common factor.

$x = \frac{H}{S M} + \frac{S M y}{S M}$

Rewrite the expression.

$x = \frac{H}{S M} + \frac{M y}{M}$

Cancel the common factor of $M$ .

Cancel the common factor.

$x = \frac{H}{S M} + \frac{M y}{M}$

Divide $y$ by $1$ .

$x = \frac{H}{S M} + y$

Solve for x H/(M(x-y))=S

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