Simplify ((x-5)/6)÷((2x-10)/12)

$\frac{x - 5}{6} \div \frac{2 x - 10}{12}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 5}{6} \cdot \frac{12}{2 x - 10}$

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$\frac{x - 5}{6} \cdot \frac{6 (2)}{2 x - 10}$

Cancel the common factor.

$\frac{x - 5}{6} \cdot \frac{6 \cdot 2}{2 x - 10}$

Rewrite the expression.

$(x - 5) \frac{2}{2 x - 10}$

Factor $2$ out of $2 x - 10$ .

Factor $2$ out of $2 x$ .

$(x - 5) \frac{2}{2 (x) - 10}$

Factor $2$ out of $- 10$ .

$(x - 5) \frac{2}{2 x + 2 \cdot - 5}$

Factor $2$ out of $2 x + 2 \cdot - 5$ .

$(x - 5) \frac{2}{2 (x - 5)}$

Cancel the common factor of $x - 5$ .

Factor $x - 5$ out of $2 (x - 5)$ .

$(x - 5) \frac{2}{(x - 5) \cdot 2}$

Cancel the common factor.

$(x - 5) \frac{2}{(x - 5) \cdot 2}$

Rewrite the expression.

$\frac{2}{2}$

Divide $2$ by $2$ .

$1$