Algebra Examples

$\frac{12}{x - 4} = 9$

Step 1

Find the LCD of the terms in the equation.

Tap for more steps...

Step 1.1

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

$x - 4, 1$

Step 1.2

Remove parentheses.

$x - 4, 1$

Step 1.3

The LCM of one and any expression is the expression.

$x - 4$

Step 2

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

Tap for more steps...

Step 2.1

Multiply each term in $\frac{12}{x - 4} = 9$ by $x - 4$ .

$\frac{12}{x - 4} (x - 4) = 9 (x - 4)$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $x - 4$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{12}{x - 4} (x - 4) = 9 (x - 4)$

Step 2.2.1.2

Rewrite the expression.

$12 = 9 (x - 4)$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Apply the distributive property.

$12 = 9 x + 9 \cdot - 4$

Step 2.3.2

Multiply $9$ by $- 4$ .

$12 = 9 x - 36$

Step 3

Solve the equation.

Tap for more steps...

Step 3.1

Rewrite the equation as $9 x - 36 = 12$ .

$9 x - 36 = 12$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Add $36$ to both sides of the equation.

$9 x = 12 + 36$

Step 3.2.2

Add $12$ and $36$ .

$9 x = 48$

Step 3.3

Divide each term in $9 x = 48$ by $9$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $9 x = 48$ by $9$ .

$\frac{9 x}{9} = \frac{48}{9}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{48}{9}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{48}{9}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Cancel the common factor of $48$ and $9$ .

Tap for more steps...

Step 3.3.3.1.1

Factor $3$ out of $48$ .

$x = \frac{3 (16)}{9}$

Step 3.3.3.1.2

Cancel the common factors.

Tap for more steps...

Step 3.3.3.1.2.1

Factor $3$ out of $9$ .

$x = \frac{3 \cdot 16}{3 \cdot 3}$

Step 3.3.3.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 16}{3 \cdot 3}$

Step 3.3.3.1.2.3

Rewrite the expression.

$x = \frac{16}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{16}{3}$

Decimal Form:

$x = 5.\overline{3}$

Mixed Number Form:

$x = 5 \frac{1}{3}$