Simplify 6/(y-1)*(5-5y)/10

$\frac{6}{y - 1} \cdot \frac{5 - 5 y}{10}$

Step 1

Factor $5$ out of $5 - 5 y$ .

Factor $5$ out of $5$ .

$\frac{6}{y - 1} \cdot \frac{5 (1) - 5 y}{10}$

Factor $5$ out of $- 5 y$ .

$\frac{6}{y - 1} \cdot \frac{5 (1) + 5 (- y)}{10}$

Factor $5$ out of $5 (1) + 5 (- y)$ .

$\frac{6}{y - 1} \cdot \frac{5 (1 - y)}{10}$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$\frac{2 (3)}{y - 1} \cdot \frac{5 (1 - y)}{10}$

Factor $2$ out of $10$ .

$\frac{2 \cdot 3}{y - 1} \cdot \frac{5 (1 - y)}{2 \cdot 5}$

Cancel the common factor.

$\frac{2 \cdot 3}{y - 1} \cdot \frac{5 (1 - y)}{2 \cdot 5}$

Rewrite the expression.

$\frac{3}{y - 1} \cdot \frac{5 (1 - y)}{5}$

Step 3

Multiply $\frac{3}{y - 1}$ by $\frac{5 (1 - y)}{5}$ .

$\frac{3 (5 (1 - y))}{(y - 1) \cdot 5}$

Step 4

Multiply $5$ by $3$ .

$\frac{15 (1 - y)}{(y - 1) \cdot 5}$

Step 5

Cancel the common factor of $15$ and $5$ .

Factor $5$ out of $15 (1 - y)$ .

$\frac{5 (3 (1 - y))}{(y - 1) \cdot 5}$

Cancel the common factors.

Factor $5$ out of $(y - 1) \cdot 5$ .

$\frac{5 (3 (1 - y))}{5 \cdot (y - 1)}$

Cancel the common factor.

$\frac{5 (3 (1 - y))}{5 \cdot (y - 1)}$

Rewrite the expression.

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

Step 6

Cancel the common factor of $1 - y$ and $y - 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

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

Factor $- 1$ out of $- y$ .

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

Factor $- 1$ out of $- 1 (- 1) - (y)$ .

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

Reorder terms.

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

Cancel the common factor.

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

Divide $3 \cdot (- 1)$ by $1$ .

$3 \cdot (- 1)$

Step 7

Multiply $3$ by $- 1$ .

$- 3$

Simplify 6/(y-1)*(5-5y)/10

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