Calculus Examples

$\frac{2 k + 8}{6} \div \frac{3 k + 12}{2}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 k + 8}{6} \cdot \frac{2}{3 k + 12}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Factor $2$ out of $6$ .

$\frac{2 k + 8}{2 (3)} \cdot \frac{2}{3 k + 12}$

Step 2.1.2

Cancel the common factor.

$\frac{2 k + 8}{2 \cdot 3} \cdot \frac{2}{3 k + 12}$

Step 2.1.3

Rewrite the expression.

$\frac{2 k + 8}{3} \cdot \frac{1}{3 k + 12}$

Step 2.2

Multiply $\frac{2 k + 8}{3}$ by $\frac{1}{3 k + 12}$ .

$\frac{2 k + 8}{3 (3 k + 12)}$

Step 2.3

Factor $2$ out of $2 k + 8$ .

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Step 2.3.1

Factor $2$ out of $2 k$ .

$\frac{2 (k) + 8}{3 (3 k + 12)}$

Step 2.3.2

Factor $2$ out of $8$ .

$\frac{2 k + 2 \cdot 4}{3 (3 k + 12)}$

Step 2.3.3

Factor $2$ out of $2 k + 2 \cdot 4$ .

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

Step 3

Simplify the denominator.

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Step 3.1

Factor $3$ out of $3 k + 12$ .

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Step 3.1.1

Factor $3$ out of $3 k$ .

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

Step 3.1.2

Factor $3$ out of $12$ .

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

Step 3.1.3

Factor $3$ out of $3 k + 3 \cdot 4$ .

$\frac{2 (k + 4)}{3 (3 (k + 4))}$

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

Step 3.2

Multiply $3$ by $3$ .

$\frac{2 (k + 4)}{9 (k + 4)}$

Step 4

Cancel the common factor of $k + 4$ .

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Step 4.1

Cancel the common factor.

$\frac{2 (k + 4)}{9 (k + 4)}$

Step 4.2

Rewrite the expression.

$\frac{2}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{9}$

Decimal Form:

$0.\overline{2}$