Simplify (z/(2z-2))÷(7/6)

$\frac{z}{2 z - 2} \div \frac{7}{6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{z}{2 z - 2} \cdot \frac{6}{7}$

Step 2

Factor $2$ out of $2 z - 2$ .

Factor $2$ out of $2 z$ .

$\frac{z}{2 (z) - 2} \cdot \frac{6}{7}$

Factor $2$ out of $- 2$ .

$\frac{z}{2 (z) + 2 (- 1)} \cdot \frac{6}{7}$

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

$\frac{z}{2 (z - 1)} \cdot \frac{6}{7}$

$\frac{z}{2 (z - 1)} \cdot \frac{6}{7}$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{z}{2 (z - 1)} \cdot \frac{2 (3)}{7}$

Cancel the common factor.

$\frac{z}{2 (z - 1)} \cdot \frac{2 \cdot 3}{7}$

Rewrite the expression.

$\frac{z}{z - 1} \cdot \frac{3}{7}$

$\frac{z}{z - 1} \cdot \frac{3}{7}$

Step 4

Multiply $\frac{z}{z - 1}$ by $\frac{3}{7}$ .

$\frac{z \cdot 3}{(z - 1) \cdot 7}$

Step 5

Reorder.

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

$\frac{3 \cdot z}{(z - 1) \cdot 7}$

Move $7$ to the left of $z - 1$ .

$\frac{3 z}{7 (z - 1)}$

$\frac{3 z}{7 (z - 1)}$

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