Algebra Examples

$\frac{3}{3} \cdot \frac{x^{2} - 36}{x - 6} \div \frac{x^{2} + 4 x - 12}{x - 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3}{3} \cdot \frac{x^{2} - 36}{x - 6} \frac{x - 2}{x^{2} + 4 x - 12}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $36$ as $6^{2}$ .

$\frac{3}{3} \cdot \frac{x^{2} - 6^{2}}{x - 6} \frac{x - 2}{x^{2} + 4 x - 12}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 6$ .

$\frac{3}{3} \cdot \frac{(x + 6) (x - 6)}{x - 6} \frac{x - 2}{x^{2} + 4 x - 12}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Divide $3$ by $3$ .

$1 \cdot \frac{(x + 6) (x - 6)}{x - 6} \frac{x - 2}{x^{2} + 4 x - 12}$

Step 3.2

Multiply $\frac{(x + 6) (x - 6)}{x - 6}$ by $1$ .

$\frac{(x + 6) (x - 6)}{x - 6} \cdot \frac{x - 2}{x^{2} + 4 x - 12}$

Step 3.3

Cancel the common factor of $x - 6$ .

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Step 3.3.1

Cancel the common factor.

$\frac{(x + 6) (x - 6)}{x - 6} \cdot \frac{x - 2}{x^{2} + 4 x - 12}$

Step 3.3.2

Divide $x + 6$ by $1$ .

$(x + 6) \frac{x - 2}{x^{2} + 4 x - 12}$

Step 4

Factor $x^{2} + 4 x - 12$ using the AC method.

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Step 4.1

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 $- 12$ and whose sum is $4$ .

$- 2, 6$

Step 4.2

Write the factored form using these integers.

$(x + 6) \frac{x - 2}{(x - 2) (x + 6)}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $x + 6$ .

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Step 5.1.1

Factor $x + 6$ out of $(x - 2) (x + 6)$ .

$(x + 6) \frac{x - 2}{(x + 6) (x - 2)}$

Step 5.1.2

Cancel the common factor.

$(x + 6) \frac{x - 2}{(x + 6) (x - 2)}$

Step 5.1.3

Rewrite the expression.

$\frac{x - 2}{x - 2}$

Step 5.2

Cancel the common factor of $x - 2$ .

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Step 5.2.1

Cancel the common factor.

$\frac{x - 2}{x - 2}$

Step 5.2.2

Rewrite the expression.

$1$