Algebra Examples

$\frac{6 a + 27}{18 a^{2} + 36 a} \div \frac{16 a + 72}{2 a + 4}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 a + 27}{18 a^{2} + 36 a} \cdot \frac{2 a + 4}{16 a + 72}$

Step 2

Factor $3$ out of $6 a + 27$ .

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Step 2.1

Factor $3$ out of $6 a$ .

$\frac{3 (2 a) + 27}{18 a^{2} + 36 a} \cdot \frac{2 a + 4}{16 a + 72}$

Step 2.2

Factor $3$ out of $27$ .

$\frac{3 (2 a) + 3 (9)}{18 a^{2} + 36 a} \cdot \frac{2 a + 4}{16 a + 72}$

Step 2.3

Factor $3$ out of $3 (2 a) + 3 (9)$ .

$\frac{3 (2 a + 9)}{18 a^{2} + 36 a} \cdot \frac{2 a + 4}{16 a + 72}$

Step 3

Factor $18 a$ out of $18 a^{2} + 36 a$ .

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Step 3.1

Factor $18 a$ out of $18 a^{2}$ .

$\frac{3 (2 a + 9)}{18 a (a) + 36 a} \cdot \frac{2 a + 4}{16 a + 72}$

Step 3.2

Factor $18 a$ out of $36 a$ .

$\frac{3 (2 a + 9)}{18 a (a) + 18 a (2)} \cdot \frac{2 a + 4}{16 a + 72}$

Step 3.3

Factor $18 a$ out of $18 a (a) + 18 a (2)$ .

$\frac{3 (2 a + 9)}{18 a (a + 2)} \cdot \frac{2 a + 4}{16 a + 72}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $3$ out of $18 a (a + 2)$ .

$\frac{3 (2 a + 9)}{3 (6 a (a + 2))} \cdot \frac{2 a + 4}{16 a + 72}$

Step 4.2

Cancel the common factor.

$\frac{3 (2 a + 9)}{3 (6 a (a + 2))} \cdot \frac{2 a + 4}{16 a + 72}$

Step 4.3

Rewrite the expression.

$\frac{2 a + 9}{6 a (a + 2)} \cdot \frac{2 a + 4}{16 a + 72}$

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $2 a + 4$ and $16 a + 72$ .

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Step 5.1.1

Factor $2$ out of $2 a$ .

$\frac{2 a + 9}{6 a (a + 2)} \cdot \frac{2 (a) + 4}{16 a + 72}$

Step 5.1.2

Factor $2$ out of $4$ .

$\frac{2 a + 9}{6 a (a + 2)} \cdot \frac{2 a + 2 \cdot 2}{16 a + 72}$

Step 5.1.3

Factor $2$ out of $2 a + 2 \cdot 2$ .

$\frac{2 a + 9}{6 a (a + 2)} \cdot \frac{2 (a + 2)}{16 a + 72}$

Step 5.1.4

Cancel the common factors.

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Step 5.1.4.1

Factor $2$ out of $16 a$ .

$\frac{2 a + 9}{6 a (a + 2)} \cdot \frac{2 (a + 2)}{2 (8 a) + 72}$

Step 5.1.4.2

Factor $2$ out of $72$ .

$\frac{2 a + 9}{6 a (a + 2)} \cdot \frac{2 (a + 2)}{2 (8 a) + 2 (36)}$

Step 5.1.4.3

Factor $2$ out of $2 (8 a) + 2 (36)$ .

$\frac{2 a + 9}{6 a (a + 2)} \cdot \frac{2 (a + 2)}{2 (8 a + 36)}$

Step 5.1.4.4

Cancel the common factor.

$\frac{2 a + 9}{6 a (a + 2)} \cdot \frac{2 (a + 2)}{2 (8 a + 36)}$

Step 5.1.4.5

Rewrite the expression.

$\frac{2 a + 9}{6 a (a + 2)} \cdot \frac{a + 2}{8 a + 36}$

Step 5.2

Cancel the common factor of $a + 2$ .

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Step 5.2.1

Factor $a + 2$ out of $6 a (a + 2)$ .

$\frac{2 a + 9}{(a + 2) (6 a)} \cdot \frac{a + 2}{8 a + 36}$

Step 5.2.2

Cancel the common factor.

$\frac{2 a + 9}{(a + 2) (6 a)} \cdot \frac{a + 2}{8 a + 36}$

Step 5.2.3

Rewrite the expression.

$\frac{2 a + 9}{6 a} \cdot \frac{1}{8 a + 36}$

Step 5.3

Multiply $\frac{2 a + 9}{6 a}$ by $\frac{1}{8 a + 36}$ .

$\frac{2 a + 9}{6 a (8 a + 36)}$

Step 6

Simplify the denominator.

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Step 6.1

Factor $4$ out of $8 a + 36$ .

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Step 6.1.1

Factor $4$ out of $8 a$ .

$\frac{2 a + 9}{6 a (4 (2 a) + 36)}$

Step 6.1.2

Factor $4$ out of $36$ .

$\frac{2 a + 9}{6 a (4 (2 a) + 4 (9))}$

Step 6.1.3

Factor $4$ out of $4 (2 a) + 4 (9)$ .

$\frac{2 a + 9}{6 a (4 (2 a + 9))}$

$\frac{2 a + 9}{6 a \cdot 4 (2 a + 9)}$

Step 6.2

Multiply $4$ by $6$ .

$\frac{2 a + 9}{24 a (2 a + 9)}$

Step 7

Cancel the common factor of $2 a + 9$ .

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Step 7.1

Cancel the common factor.

$\frac{2 a + 9}{24 a (2 a + 9)}$

Step 7.2

Rewrite the expression.

$\frac{1}{24 a}$