Algebra Examples

$\frac{x + 2}{x - 4} \div \frac{1}{3 x - 12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 2}{x - 4} (3 x - 12)$

Step 2

Multiply $\frac{x + 2}{x - 4}$ by $3 x - 12$ .

$\frac{(x + 2) (3 x - 12)}{x - 4}$

Step 3

Factor $3$ out of $3 x - 12$ .

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Step 3.1

Factor $3$ out of $3 x$ .

$\frac{(x + 2) (3 (x) - 12)}{x - 4}$

Step 3.2

Factor $3$ out of $- 12$ .

$\frac{(x + 2) (3 x + 3 \cdot - 4)}{x - 4}$

Step 3.3

Factor $3$ out of $3 x + 3 \cdot - 4$ .

$\frac{(x + 2) (3 (x - 4))}{x - 4}$

$\frac{(x + 2) \cdot 3 (x - 4)}{x - 4}$

Step 4

Cancel the common factor of $x - 4$ .

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Step 4.1

Cancel the common factor.

$\frac{(x + 2) \cdot 3 (x - 4)}{x - 4}$

Step 4.2

Divide $(x + 2) \cdot 3$ by $1$ .

$(x + 2) \cdot 3$

$(x + 2) \cdot 3$

Step 5

Apply the distributive property.

$x \cdot 3 + 2 \cdot 3$

Step 6

Move $3$ to the left of $x$ .

$3 \cdot x + 2 \cdot 3$

Step 7

Multiply $2$ by $3$ .

$3 x + 6$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$