Algebra Examples

$\frac{7 x + 21}{x^{2} + 5 x + 6} \div \frac{x + 6}{x + 2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{7 x + 21}{x^{2} + 5 x + 6} \cdot \frac{x + 2}{x + 6}$

Step 2

Factor $7$ out of $7 x + 21$ .

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Step 2.1

Factor $7$ out of $7 x$ .

$\frac{7 (x) + 21}{x^{2} + 5 x + 6} \cdot \frac{x + 2}{x + 6}$

Step 2.2

Factor $7$ out of $21$ .

$\frac{7 x + 7 \cdot 3}{x^{2} + 5 x + 6} \cdot \frac{x + 2}{x + 6}$

Step 2.3

Factor $7$ out of $7 x + 7 \cdot 3$ .

$\frac{7 (x + 3)}{x^{2} + 5 x + 6} \cdot \frac{x + 2}{x + 6}$

Step 3

Factor $x^{2} + 5 x + 6$ 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 $6$ and whose sum is $5$ .

$2, 3$

Step 3.2

Write the factored form using these integers.

$\frac{7 (x + 3)}{(x + 2) (x + 3)} \cdot \frac{x + 2}{x + 6}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $x + 2$ .

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Step 4.1.1

Cancel the common factor.

$\frac{7 (x + 3)}{(x + 2) (x + 3)} \cdot \frac{x + 2}{x + 6}$

Step 4.1.2

Rewrite the expression.

$\frac{7 (x + 3)}{x + 3} \cdot \frac{1}{x + 6}$

Step 4.2

Multiply $\frac{7 (x + 3)}{x + 3}$ by $\frac{1}{x + 6}$ .

$\frac{7 (x + 3)}{(x + 3) (x + 6)}$

Step 4.3

Cancel the common factor of $x + 3$ .

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Step 4.3.1

Cancel the common factor.

$\frac{7 (x + 3)}{(x + 3) (x + 6)}$

Step 4.3.2

Rewrite the expression.

$\frac{7}{x + 6}$