Solve for y w=(x+6)/(y+z)

$w = \frac{x + 6}{y + z}$

Step 1

Rewrite the equation as $\frac{x + 6}{y + z} = w$ .

$\frac{x + 6}{y + z} = w$

Step 2

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.

$y + z, 1$

Remove parentheses.

$y + z, 1$

The LCM of one and any expression is the expression.

$y + z$

Step 3

Multiply each term in $\frac{x + 6}{y + z} = w$ by $y + z$ to eliminate the fractions.

Multiply each term in $\frac{x + 6}{y + z} = w$ by $y + z$ .

$\frac{x + 6}{y + z} (y + z) = w (y + z)$

Simplify the left side.

Cancel the common factor of $y + z$ .

Cancel the common factor.

$\frac{x + 6}{y + z} (y + z) = w (y + z)$

Rewrite the expression.

$x + 6 = w (y + z)$

Simplify the right side.

Apply the distributive property.

$x + 6 = w y + w z$

Step 4

Solve the equation.

Rewrite the equation as $w y + w z = x + 6$ .

$w y + w z = x + 6$

Subtract $w z$ from both sides of the equation.

$w y = x + 6 - w z$

Divide each term in $w y = x + 6 - w z$ by $w$ and simplify.

Divide each term in $w y = x + 6 - w z$ by $w$ .

$\frac{w y}{w} = \frac{x}{w} + \frac{6}{w} + \frac{- w z}{w}$

Simplify the left side.

Cancel the common factor of $w$ .

Cancel the common factor.

$\frac{w y}{w} = \frac{x}{w} + \frac{6}{w} + \frac{- w z}{w}$

Divide $y$ by $1$ .

$y = \frac{x}{w} + \frac{6}{w} + \frac{- w z}{w}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $w$ .

Cancel the common factor.

$y = \frac{x}{w} + \frac{6}{w} + \frac{- w z}{w}$

Divide $- 1 z$ by $1$ .

$y = \frac{x}{w} + \frac{6}{w} - 1 z$

Rewrite $- 1 z$ as $- z$ .

$y = \frac{x}{w} + \frac{6}{w} - z$

Solve for y w=(x+6)/(y+z)

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