Simplify (z/(z-1))÷(1/(3z-3))

$\frac{z}{z - 1} \div \frac{1}{3 z - 3}$

To divide by a fraction, multiply by its reciprocal.

$\frac{z}{z - 1} (3 z - 3)$

Multiply $\frac{z}{z - 1}$ by $3 z - 3$ .

$\frac{z (3 z - 3)}{z - 1}$

Factor $3$ out of $3 z - 3$ .

Factor $3$ out of $3 z$ .

$\frac{z (3 (z) - 3)}{z - 1}$

Factor $3$ out of $- 3$ .

$\frac{z (3 (z) + 3 (- 1))}{z - 1}$

Factor $3$ out of $3 (z) + 3 (- 1)$ .

$\frac{z (3 (z - 1))}{z - 1}$

$\frac{z \cdot 3 (z - 1)}{z - 1}$

Cancel the common factor of $z - 1$ .

Cancel the common factor.

$\frac{z \cdot 3 (z - 1)}{z - 1}$

Divide $z \cdot 3$ by $1$ .

$z \cdot 3$

Move $3$ to the left of $z$ .

$3 z$