Algebra Examples

$\frac{20 - 25 x}{15} \cdot \frac{3 x + 9}{8 - 10 x}$

Step 1

Factor $5$ out of $20 - 25 x$ .

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Step 1.1

Factor $5$ out of $20$ .

$\frac{5 (4) - 25 x}{15} \cdot \frac{3 x + 9}{8 - 10 x}$

Step 1.2

Factor $5$ out of $- 25 x$ .

$\frac{5 (4) + 5 (- 5 x)}{15} \cdot \frac{3 x + 9}{8 - 10 x}$

Step 1.3

Factor $5$ out of $5 (4) + 5 (- 5 x)$ .

$\frac{5 (4 - 5 x)}{15} \cdot \frac{3 x + 9}{8 - 10 x}$

Step 2

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

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Step 2.1

Factor $3$ out of $3 x$ .

$\frac{5 (4 - 5 x)}{15} \cdot \frac{3 (x) + 9}{8 - 10 x}$

Step 2.2

Factor $3$ out of $9$ .

$\frac{5 (4 - 5 x)}{15} \cdot \frac{3 x + 3 \cdot 3}{8 - 10 x}$

Step 2.3

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

$\frac{5 (4 - 5 x)}{15} \cdot \frac{3 (x + 3)}{8 - 10 x}$

Step 3

Factor $2$ out of $8 - 10 x$ .

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Step 3.1

Factor $2$ out of $8$ .

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

Step 3.2

Factor $2$ out of $- 10 x$ .

$\frac{5 (4 - 5 x)}{15} \cdot \frac{3 (x + 3)}{2 (4) + 2 (- 5 x)}$

Step 3.3

Factor $2$ out of $2 (4) + 2 (- 5 x)$ .

$\frac{5 (4 - 5 x)}{15} \cdot \frac{3 (x + 3)}{2 (4 - 5 x)}$

Step 4

Cancel the common factor of $4 - 5 x$ .

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Step 4.1

Factor $4 - 5 x$ out of $5 (4 - 5 x)$ .

$\frac{(4 - 5 x) \cdot 5}{15} \cdot \frac{3 (x + 3)}{2 (4 - 5 x)}$

Step 4.2

Factor $4 - 5 x$ out of $2 (4 - 5 x)$ .

$\frac{(4 - 5 x) \cdot 5}{15} \cdot \frac{3 (x + 3)}{(4 - 5 x) \cdot 2}$

Step 4.3

Cancel the common factor.

$\frac{(4 - 5 x) \cdot 5}{15} \cdot \frac{3 (x + 3)}{(4 - 5 x) \cdot 2}$

Step 4.4

Rewrite the expression.

$\frac{5}{15} \cdot \frac{3 (x + 3)}{2}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $15$ .

$\frac{5}{3 (5)} \cdot \frac{3 (x + 3)}{2}$

Step 5.2

Cancel the common factor.

$\frac{5}{3 \cdot 5} \cdot \frac{3 (x + 3)}{2}$

Step 5.3

Rewrite the expression.

$\frac{5}{5} \cdot \frac{x + 3}{2}$

Step 6

Multiply $\frac{5}{5}$ by $\frac{x + 3}{2}$ .

$\frac{5 (x + 3)}{5 \cdot 2}$

Step 7

Multiply $5$ by $2$ .

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

Step 8

Cancel the common factors.

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Step 8.1

Factor $5$ out of $10$ .

$\frac{5 (x + 3)}{5 \cdot 2}$

Step 8.2

Cancel the common factor.

$\frac{5 (x + 3)}{5 \cdot 2}$

Step 8.3

Rewrite the expression.

$\frac{x + 3}{2}$