Divide ((x-1)/3)÷((2x-2)/6)

$\frac{x - 1}{3} \div \frac{2 x - 2}{6}$

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 1}{3} \cdot \frac{6}{2 x - 2}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{x - 1}{3} \cdot \frac{3 (2)}{2 x - 2}$

Cancel the common factor.

$\frac{x - 1}{3} \cdot \frac{3 \cdot 2}{2 x - 2}$

Rewrite the expression.

$(x - 1) \frac{2}{2 x - 2}$

$(x - 1) \frac{2}{2 x - 2}$

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

Factor $2$ out of $2 x$ .

$(x - 1) \frac{2}{2 (x) - 2}$

Factor $2$ out of $- 2$ .

$(x - 1) \frac{2}{2 (x) + 2 (- 1)}$

Factor $2$ out of $2 (x) + 2 (- 1)$ .

$(x - 1) \frac{2}{2 (x - 1)}$

$(x - 1) \frac{2}{2 (x - 1)}$

Cancel the common factor of $x - 1$ .

Factor $x - 1$ out of $2 (x - 1)$ .

$(x - 1) \frac{2}{(x - 1) \cdot 2}$

Cancel the common factor.

$(x - 1) \frac{2}{(x - 1) \cdot 2}$

Rewrite the expression.

$\frac{2}{2}$

$\frac{2}{2}$

Divide $2$ by $2$ .

$1$

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