Simplify (5y-20)/(3y+15)*(7y+35)/(10y+40)

$\frac{5 y - 20}{3 y + 15} \cdot \frac{7 y + 35}{10 y + 40}$

Step 1

Factor $5$ out of $5 y - 20$ .

Factor $5$ out of $5 y$ .

$\frac{5 (y) - 20}{3 y + 15} \cdot \frac{7 y + 35}{10 y + 40}$

Factor $5$ out of $- 20$ .

$\frac{5 y + 5 \cdot - 4}{3 y + 15} \cdot \frac{7 y + 35}{10 y + 40}$

Factor $5$ out of $5 y + 5 \cdot - 4$ .

$\frac{5 (y - 4)}{3 y + 15} \cdot \frac{7 y + 35}{10 y + 40}$

Step 2

Factor $3$ out of $3 y + 15$ .

Factor $3$ out of $3 y$ .

$\frac{5 (y - 4)}{3 (y) + 15} \cdot \frac{7 y + 35}{10 y + 40}$

Factor $3$ out of $15$ .

$\frac{5 (y - 4)}{3 y + 3 \cdot 5} \cdot \frac{7 y + 35}{10 y + 40}$

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

$\frac{5 (y - 4)}{3 (y + 5)} \cdot \frac{7 y + 35}{10 y + 40}$

Step 3

Factor $7$ out of $7 y + 35$ .

Factor $7$ out of $7 y$ .

$\frac{5 (y - 4)}{3 (y + 5)} \cdot \frac{7 (y) + 35}{10 y + 40}$

Factor $7$ out of $35$ .

$\frac{5 (y - 4)}{3 (y + 5)} \cdot \frac{7 y + 7 \cdot 5}{10 y + 40}$

Factor $7$ out of $7 y + 7 \cdot 5$ .

$\frac{5 (y - 4)}{3 (y + 5)} \cdot \frac{7 (y + 5)}{10 y + 40}$

Step 4

Factor $10$ out of $10 y + 40$ .

Factor $10$ out of $10 y$ .

$\frac{5 (y - 4)}{3 (y + 5)} \cdot \frac{7 (y + 5)}{10 (y) + 40}$

Factor $10$ out of $40$ .

$\frac{5 (y - 4)}{3 (y + 5)} \cdot \frac{7 (y + 5)}{10 y + 10 \cdot 4}$

Factor $10$ out of $10 y + 10 \cdot 4$ .

$\frac{5 (y - 4)}{3 (y + 5)} \cdot \frac{7 (y + 5)}{10 (y + 4)}$

Step 5

Cancel the common factor of $5$ .

Factor $5$ out of $10 (y + 4)$ .

$\frac{5 (y - 4)}{3 (y + 5)} \cdot \frac{7 (y + 5)}{5 (2 (y + 4))}$

Cancel the common factor.

$\frac{5 (y - 4)}{3 (y + 5)} \cdot \frac{7 (y + 5)}{5 (2 (y + 4))}$

Rewrite the expression.

$\frac{y - 4}{3 (y + 5)} \cdot \frac{7 (y + 5)}{2 (y + 4)}$

Step 6

Cancel the common factor of $y + 5$ .

Factor $y + 5$ out of $3 (y + 5)$ .

$\frac{y - 4}{(y + 5) \cdot 3} \cdot \frac{7 (y + 5)}{2 (y + 4)}$

Factor $y + 5$ out of $7 (y + 5)$ .

$\frac{y - 4}{(y + 5) \cdot 3} \cdot \frac{(y + 5) \cdot 7}{2 (y + 4)}$

Cancel the common factor.

$\frac{y - 4}{(y + 5) \cdot 3} \cdot \frac{(y + 5) \cdot 7}{2 (y + 4)}$

Rewrite the expression.

$\frac{y - 4}{3} \cdot \frac{7}{2 (y + 4)}$

Step 7

Multiply $\frac{y - 4}{3}$ by $\frac{7}{2 (y + 4)}$ .

$\frac{(y - 4) \cdot 7}{3 (2 (y + 4))}$

Step 8

Simplify the expression.

Multiply $2$ by $3$ .

$\frac{(y - 4) \cdot 7}{6 (y + 4)}$

Move $7$ to the left of $y - 4$ .

$\frac{7 (y - 4)}{6 (y + 4)}$

Simplify (5y-20)/(3y+15)*(7y+35)/(10y+40)

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