Solve for y w=z/(3y-x) ; solve for y

$w = \frac{z}{3 y - x}$ ; solve for $y$

Rewrite the equation as $\frac{z}{3 y - x} = w$ .

$\frac{z}{3 y - x} = w$

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.

$3 y - x, 1$

Remove parentheses.

$3 y - x, 1$

The LCM of one and any expression is the expression.

$3 y - x$

Multiply each term in $\frac{z}{3 y - x} = w$ by $3 y - x$ to eliminate the fractions.

Multiply each term in $\frac{z}{3 y - x} = w$ by $3 y - x$ .

$\frac{z}{3 y - x} (3 y - x) = w (3 y - x)$

Simplify the left side.

Cancel the common factor of $3 y - x$ .

Cancel the common factor.

$\frac{z}{3 y - x} (3 y - x) = w (3 y - x)$

Rewrite the expression.

$z = w (3 y - x)$

Simplify the right side.

Apply the distributive property.

$z = w (3 y) + w (- x)$

Reorder.

Rewrite using the commutative property of multiplication.

$z = 3 w y + w (- x)$

Rewrite using the commutative property of multiplication.

$z = 3 w y - w x$

Solve the equation.

Rewrite the equation as $3 w y - w x = z$ .

$3 w y - w x = z$

Add $w x$ to both sides of the equation.

$3 w y = z + w x$

Divide each term in $3 w y = z + w x$ by $3 w$ and simplify.

Divide each term in $3 w y = z + w x$ by $3 w$ .

$\frac{3 w y}{3 w} = \frac{z}{3 w} + \frac{w x}{3 w}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 w y}{3 w} = \frac{z}{3 w} + \frac{w x}{3 w}$

Rewrite the expression.

$\frac{w y}{w} = \frac{z}{3 w} + \frac{w x}{3 w}$

Cancel the common factor of $w$ .

Cancel the common factor.

$\frac{w y}{w} = \frac{z}{3 w} + \frac{w x}{3 w}$

Divide $y$ by $1$ .

$y = \frac{z}{3 w} + \frac{w x}{3 w}$

Simplify the right side.

Cancel the common factor of $w$ .

Cancel the common factor.

$y = \frac{z}{3 w} + \frac{w x}{3 w}$

Rewrite the expression.

$y = \frac{z}{3 w} + \frac{x}{3}$

Solve for y w=z/(3y-x) ; solve for y

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