Solve for a 8/4=16/(a-4)

$\frac{8}{4} = \frac{16}{a - 4}$

Step 1

Rewrite the equation as $\frac{16}{a - 4} = \frac{8}{4}$ .

$\frac{16}{a - 4} = \frac{8}{4}$

Step 2

Divide $8$ by $4$ .

$\frac{16}{a - 4} = 2$

Step 3

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.

$a - 4, 1$

Remove parentheses.

$a - 4, 1$

The LCM of one and any expression is the expression.

$a - 4$

Step 4

Multiply each term in $\frac{16}{a - 4} = 2$ by $a - 4$ to eliminate the fractions.

Multiply each term in $\frac{16}{a - 4} = 2$ by $a - 4$ .

$\frac{16}{a - 4} (a - 4) = 2 (a - 4)$

Simplify the left side.

Cancel the common factor of $a - 4$ .

Cancel the common factor.

$\frac{16}{a - 4} (a - 4) = 2 (a - 4)$

Rewrite the expression.

$16 = 2 (a - 4)$

Simplify the right side.

Apply the distributive property.

$16 = 2 a + 2 \cdot - 4$

Multiply $2$ by $- 4$ .

$16 = 2 a - 8$

Step 5

Solve the equation.

Rewrite the equation as $2 a - 8 = 16$ .

$2 a - 8 = 16$

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

Add $8$ to both sides of the equation.

$2 a = 16 + 8$

Add $16$ and $8$ .

$2 a = 24$

Divide each term in $2 a = 24$ by $2$ and simplify.

Divide each term in $2 a = 24$ by $2$ .

$\frac{2 a}{2} = \frac{24}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a}{2} = \frac{24}{2}$

Divide $a$ by $1$ .

$a = \frac{24}{2}$

Simplify the right side.

Divide $24$ by $2$ .

$a = 12$

Solve for a 8/4=16/(a-4)

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