Simplify (5x-10)/6*12/(3x-6)

$\frac{5 x - 10}{6} \cdot \frac{12}{3 x - 6}$

Factor $5$ out of $5 x - 10$ .

Factor $5$ out of $5 x$ .

$\frac{5 (x) - 10}{6} \cdot \frac{12}{3 x - 6}$

Factor $5$ out of $- 10$ .

$\frac{5 x + 5 \cdot - 2}{6} \cdot \frac{12}{3 x - 6}$

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

$\frac{5 (x - 2)}{6} \cdot \frac{12}{3 x - 6}$

Factor $3$ out of $3 x - 6$ .

Factor $3$ out of $3 x$ .

$\frac{5 (x - 2)}{6} \cdot \frac{12}{3 (x) - 6}$

Factor $3$ out of $- 6$ .

$\frac{5 (x - 2)}{6} \cdot \frac{12}{3 x + 3 \cdot - 2}$

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{5 (x - 2)}{6} \cdot \frac{12}{3 (x - 2)}$

Cancel the common factor of $x - 2$ .

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

$\frac{(x - 2) \cdot 5}{6} \cdot \frac{12}{3 (x - 2)}$

Factor $x - 2$ out of $3 (x - 2)$ .

$\frac{(x - 2) \cdot 5}{6} \cdot \frac{12}{(x - 2) \cdot 3}$

Cancel the common factor.

$\frac{(x - 2) \cdot 5}{6} \cdot \frac{12}{(x - 2) \cdot 3}$

Rewrite the expression.

$\frac{5}{6} \cdot \frac{12}{3}$

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$\frac{5}{6} \cdot \frac{6 (2)}{3}$

Cancel the common factor.

$\frac{5}{6} \cdot \frac{6 \cdot 2}{3}$

Rewrite the expression.

$5 \cdot \frac{2}{3}$

Combine $5$ and $\frac{2}{3}$ .

$\frac{5 \cdot 2}{3}$

Multiply $5$ by $2$ .

$\frac{10}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{3}$

Decimal Form:

$3.\overline{3}$

Mixed Number Form:

$3 \frac{1}{3}$