Simplify (3/(6p+18))÷(1/(p+3))

$\frac{3}{6 p + 18} \div \frac{1}{p + 3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3}{6 p + 18} (p + 3)$

Step 2

Cancel the common factor of $3$ and $6 p + 18$ .

Factor $3$ out of $3$ .

$\frac{3 (1)}{6 p + 18} (p + 3)$

Cancel the common factors.

Factor $3$ out of $6 p$ .

$\frac{3 (1)}{3 (2 p) + 18} (p + 3)$

Factor $3$ out of $18$ .

$\frac{3 \cdot 1}{3 (2 p) + 3 \cdot 6} (p + 3)$

Factor $3$ out of $3 (2 p) + 3 (6)$ .

$\frac{3 (1)}{3 (2 p + 6)} (p + 3)$

Cancel the common factor.

$\frac{3 \cdot 1}{3 (2 p + 6)} (p + 3)$

Rewrite the expression.

$\frac{1}{2 p + 6} (p + 3)$

$\frac{1}{2 p + 6} (p + 3)$

$\frac{1}{2 p + 6} (p + 3)$

Step 3

Factor $2$ out of $2 p + 6$ .

Factor $2$ out of $2 p$ .

$\frac{1}{2 (p) + 6} (p + 3)$

Factor $2$ out of $6$ .

$\frac{1}{2 p + 2 \cdot 3} (p + 3)$

Factor $2$ out of $2 p + 2 \cdot 3$ .

$\frac{1}{2 (p + 3)} (p + 3)$

$\frac{1}{2 (p + 3)} (p + 3)$

Step 4

Cancel the common factor of $p + 3$ .

Factor $p + 3$ out of $2 (p + 3)$ .

$\frac{1}{(p + 3) \cdot 2} (p + 3)$

Cancel the common factor.

$\frac{1}{(p + 3) \cdot 2} (p + 3)$

Rewrite the expression.

$\frac{1}{2}$

$\frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

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