Basic Math Examples

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

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.

Tap for more steps...

Step 2.1

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

$y + z, 1$

Step 2.2

Remove parentheses.

$y + z, 1$

Step 2.3

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.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $y + z$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Rewrite the expression.

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

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Apply the distributive property.

$x + 6 = w y + w z$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

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

$w y + w z = x + 6$

Step 4.2

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

$w z = x + 6 - w y$

Step 4.3

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

Tap for more steps...

Step 4.3.1

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

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

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $w$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

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

Step 4.3.2.1.2

Divide $z$ by $1$ .

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

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Simplify each term.

Tap for more steps...

Step 4.3.3.1.1

Cancel the common factor of $w$ .

Tap for more steps...

Step 4.3.3.1.1.1

Cancel the common factor.

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

Step 4.3.3.1.1.2

Divide $- 1 y$ by $1$ .

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

Step 4.3.3.1.2

Rewrite $- 1 y$ as $- y$ .

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