Simplify ((x+3)/12)÷((9x+27)/24)

$\frac{x + 3}{12} \div \frac{9 x + 27}{24}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 3}{12} \cdot \frac{24}{9 x + 27}$

Cancel the common factor of $12$ .

Factor $12$ out of $24$ .

$\frac{x + 3}{12} \cdot \frac{12 (2)}{9 x + 27}$

Cancel the common factor.

$\frac{x + 3}{12} \cdot \frac{12 \cdot 2}{9 x + 27}$

Rewrite the expression.

$(x + 3) \frac{2}{9 x + 27}$

Factor $9$ out of $9 x + 27$ .

Factor $9$ out of $9 x$ .

$(x + 3) \frac{2}{9 (x) + 27}$

Factor $9$ out of $27$ .

$(x + 3) \frac{2}{9 x + 9 \cdot 3}$

Factor $9$ out of $9 x + 9 \cdot 3$ .

$(x + 3) \frac{2}{9 (x + 3)}$

Cancel the common factor of $x + 3$ .

Factor $x + 3$ out of $9 (x + 3)$ .

$(x + 3) \frac{2}{(x + 3) \cdot 9}$

Cancel the common factor.

$(x + 3) \frac{2}{(x + 3) \cdot 9}$

Rewrite the expression.

$\frac{2}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{9}$

Decimal Form:

$0.\overline{2}$