Pre-Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 3}{4 x - 12} \cdot \frac{x^{2} - 2 x - 3}{x - 2}$

Step 2

Factor $4$ out of $4 x - 12$ .

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Step 2.1

Factor $4$ out of $4 x$ .

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

Step 2.2

Factor $4$ out of $- 12$ .

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

Step 2.3

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

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

Step 3

Factor $x^{2} - 2 x - 3$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 3$ and whose sum is $- 2$ .

$- 3, 1$

Step 3.2

Write the factored form using these integers.

$\frac{x + 3}{4 (x - 3)} \cdot \frac{(x - 3) (x + 1)}{x - 2}$

Step 4

Cancel the common factor of $x - 3$ .

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Step 4.1

Factor $x - 3$ out of $4 (x - 3)$ .

$\frac{x + 3}{(x - 3) \cdot 4} \cdot \frac{(x - 3) (x + 1)}{x - 2}$

Step 4.2

Cancel the common factor.

$\frac{x + 3}{(x - 3) \cdot 4} \cdot \frac{(x - 3) (x + 1)}{x - 2}$

Step 4.3

Rewrite the expression.

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

Step 5

Multiply $\frac{x + 3}{4}$ by $\frac{x + 1}{x - 2}$ .

$\frac{(x + 3) (x + 1)}{4 (x - 2)}$