Algebra Examples

$\frac{8 y - 4}{10 y - 5} \cdot \frac{5 y - 15}{3 y - 9}$

Step 1

Factor $4$ out of $8 y - 4$ .

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Step 1.1

Factor $4$ out of $8 y$ .

$\frac{4 (2 y) - 4}{10 y - 5} \cdot \frac{5 y - 15}{3 y - 9}$

Step 1.2

Factor $4$ out of $- 4$ .

$\frac{4 (2 y) + 4 (- 1)}{10 y - 5} \cdot \frac{5 y - 15}{3 y - 9}$

Step 1.3

Factor $4$ out of $4 (2 y) + 4 (- 1)$ .

$\frac{4 (2 y - 1)}{10 y - 5} \cdot \frac{5 y - 15}{3 y - 9}$

Step 2

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

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Step 2.1

Factor $5$ out of $10 y$ .

$\frac{4 (2 y - 1)}{5 (2 y) - 5} \cdot \frac{5 y - 15}{3 y - 9}$

Step 2.2

Factor $5$ out of $- 5$ .

$\frac{4 (2 y - 1)}{5 (2 y) + 5 (- 1)} \cdot \frac{5 y - 15}{3 y - 9}$

Step 2.3

Factor $5$ out of $5 (2 y) + 5 (- 1)$ .

$\frac{4 (2 y - 1)}{5 (2 y - 1)} \cdot \frac{5 y - 15}{3 y - 9}$

Step 3

Factor $5$ out of $5 y - 15$ .

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Step 3.1

Factor $5$ out of $5 y$ .

$\frac{4 (2 y - 1)}{5 (2 y - 1)} \cdot \frac{5 (y) - 15}{3 y - 9}$

Step 3.2

Factor $5$ out of $- 15$ .

$\frac{4 (2 y - 1)}{5 (2 y - 1)} \cdot \frac{5 y + 5 \cdot - 3}{3 y - 9}$

Step 3.3

Factor $5$ out of $5 y + 5 \cdot - 3$ .

$\frac{4 (2 y - 1)}{5 (2 y - 1)} \cdot \frac{5 (y - 3)}{3 y - 9}$

Step 4

Factor $3$ out of $3 y - 9$ .

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Step 4.1

Factor $3$ out of $3 y$ .

$\frac{4 (2 y - 1)}{5 (2 y - 1)} \cdot \frac{5 (y - 3)}{3 (y) - 9}$

Step 4.2

Factor $3$ out of $- 9$ .

$\frac{4 (2 y - 1)}{5 (2 y - 1)} \cdot \frac{5 (y - 3)}{3 y + 3 \cdot - 3}$

Step 4.3

Factor $3$ out of $3 y + 3 \cdot - 3$ .

$\frac{4 (2 y - 1)}{5 (2 y - 1)} \cdot \frac{5 (y - 3)}{3 (y - 3)}$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Cancel the common factor.

$\frac{4 (2 y - 1)}{5 (2 y - 1)} \cdot \frac{5 (y - 3)}{3 (y - 3)}$

Step 5.2

Rewrite the expression.

$\frac{4 (2 y - 1)}{2 y - 1} \cdot \frac{y - 3}{3 (y - 3)}$

Step 6

Multiply $\frac{4 (2 y - 1)}{2 y - 1}$ by $\frac{y - 3}{3 (y - 3)}$ .

$\frac{4 (2 y - 1) (y - 3)}{(2 y - 1) (3 (y - 3))}$

Step 7

Cancel the common factor of $2 y - 1$ .

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Step 7.1

Cancel the common factor.

$\frac{4 (2 y - 1) (y - 3)}{(2 y - 1) (3 (y - 3))}$

Step 7.2

Rewrite the expression.

$\frac{4 (y - 3)}{3 (y - 3)}$

Step 8

Cancel the common factor of $y - 3$ .

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Step 8.1

Cancel the common factor.

$\frac{4 (y - 3)}{3 (y - 3)}$

Step 8.2

Rewrite the expression.

$\frac{4}{3}$