Solve for v 9=(v+4)/(v+12)

$9 = \frac{v + 4}{v + 12}$

Step 1

Rewrite the equation as $\frac{v + 4}{v + 12} = 9$ .

$\frac{v + 4}{v + 12} = 9$

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.

$v + 12, 1$

Remove parentheses.

$v + 12, 1$

The LCM of one and any expression is the expression.

$v + 12$

Step 3

Multiply each term in $\frac{v + 4}{v + 12} = 9$ by $v + 12$ to eliminate the fractions.

Multiply each term in $\frac{v + 4}{v + 12} = 9$ by $v + 12$ .

$\frac{v + 4}{v + 12} (v + 12) = 9 (v + 12)$

Simplify the left side.

Cancel the common factor of $v + 12$ .

Cancel the common factor.

$\frac{v + 4}{v + 12} (v + 12) = 9 (v + 12)$

Rewrite the expression.

$v + 4 = 9 (v + 12)$

Simplify the right side.

Apply the distributive property.

$v + 4 = 9 v + 9 \cdot 12$

Multiply $9$ by $12$ .

$v + 4 = 9 v + 108$

Step 4

Solve the equation.

Move all terms containing $v$ to the left side of the equation.

Subtract $9 v$ from both sides of the equation.

$v + 4 - 9 v = 108$

Subtract $9 v$ from $v$ .

$- 8 v + 4 = 108$

Move all terms not containing $v$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$- 8 v = 108 - 4$

Subtract $4$ from $108$ .

$- 8 v = 104$

Divide each term in $- 8 v = 104$ by $- 8$ and simplify.

Divide each term in $- 8 v = 104$ by $- 8$ .

$\frac{- 8 v}{- 8} = \frac{104}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 v}{- 8} = \frac{104}{- 8}$

Divide $v$ by $1$ .

$v = \frac{104}{- 8}$

Simplify the right side.

Divide $104$ by $- 8$ .

$v = - 13$

Solve for v 9=(v+4)/(v+12)

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