Simplify (3x-9)/(5x+15)*(14x+42)/(10x-30)

$\frac{3 x - 9}{5 x + 15} \cdot \frac{14 x + 42}{10 x - 30}$

Step 1

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

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 9}{5 x + 15} \cdot \frac{14 x + 42}{10 x - 30}$

Factor $3$ out of $- 9$ .

$\frac{3 x + 3 \cdot - 3}{5 x + 15} \cdot \frac{14 x + 42}{10 x - 30}$

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

$\frac{3 (x - 3)}{5 x + 15} \cdot \frac{14 x + 42}{10 x - 30}$

Step 2

Factor $5$ out of $5 x + 15$ .

Factor $5$ out of $5 x$ .

$\frac{3 (x - 3)}{5 (x) + 15} \cdot \frac{14 x + 42}{10 x - 30}$

Factor $5$ out of $15$ .

$\frac{3 (x - 3)}{5 x + 5 \cdot 3} \cdot \frac{14 x + 42}{10 x - 30}$

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

$\frac{3 (x - 3)}{5 (x + 3)} \cdot \frac{14 x + 42}{10 x - 30}$

Step 3

Factor $14$ out of $14 x + 42$ .

Factor $14$ out of $14 x$ .

$\frac{3 (x - 3)}{5 (x + 3)} \cdot \frac{14 (x) + 42}{10 x - 30}$

Factor $14$ out of $42$ .

$\frac{3 (x - 3)}{5 (x + 3)} \cdot \frac{14 x + 14 \cdot 3}{10 x - 30}$

Factor $14$ out of $14 x + 14 \cdot 3$ .

$\frac{3 (x - 3)}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10 x - 30}$

Step 4

Factor $10$ out of $10 x - 30$ .

Factor $10$ out of $10 x$ .

$\frac{3 (x - 3)}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10 (x) - 30}$

Factor $10$ out of $- 30$ .

$\frac{3 (x - 3)}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10 x + 10 \cdot - 3}$

Factor $10$ out of $10 x + 10 \cdot - 3$ .

$\frac{3 (x - 3)}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10 (x - 3)}$

Step 5

Cancel the common factor of $x - 3$ .

Factor $x - 3$ out of $3 (x - 3)$ .

$\frac{(x - 3) \cdot 3}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10 (x - 3)}$

Factor $x - 3$ out of $10 (x - 3)$ .

$\frac{(x - 3) \cdot 3}{5 (x + 3)} \cdot \frac{14 (x + 3)}{(x - 3) \cdot 10}$

Cancel the common factor.

$\frac{(x - 3) \cdot 3}{5 (x + 3)} \cdot \frac{14 (x + 3)}{(x - 3) \cdot 10}$

Rewrite the expression.

$\frac{3}{5 (x + 3)} \cdot \frac{14 (x + 3)}{10}$

Step 6

Cancel the common factor of $x + 3$ .

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

$\frac{3}{(x + 3) \cdot 5} \cdot \frac{14 (x + 3)}{10}$

Factor $x + 3$ out of $14 (x + 3)$ .

$\frac{3}{(x + 3) \cdot 5} \cdot \frac{(x + 3) \cdot 14}{10}$

Cancel the common factor.

$\frac{3}{(x + 3) \cdot 5} \cdot \frac{(x + 3) \cdot 14}{10}$

Rewrite the expression.

$\frac{3}{5} \cdot \frac{14}{10}$

Step 7

Multiply $\frac{3}{5}$ by $\frac{14}{10}$ .

$\frac{3 \cdot 14}{5 \cdot 10}$

Step 8

Multiply.

Multiply $3$ by $14$ .

$\frac{42}{5 \cdot 10}$

Multiply $5$ by $10$ .

$\frac{42}{50}$

Step 9

Cancel the common factor of $42$ and $50$ .

Factor $2$ out of $42$ .

$\frac{2 (21)}{50}$

Cancel the common factors.

Factor $2$ out of $50$ .

$\frac{2 \cdot 21}{2 \cdot 25}$

Cancel the common factor.

$\frac{2 \cdot 21}{2 \cdot 25}$

Rewrite the expression.

$\frac{21}{25}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{21}{25}$

Decimal Form:

$0.84$

Simplify (3x-9)/(5x+15)*(14x+42)/(10x-30)

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