Algebra Examples

$\frac{2 x + 4}{10 x} \cdot \frac{15 x^{2}}{x + 2}$

Step 1

Factor $2$ out of $2 x + 4$ .

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Step 1.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 4}{10 x} \cdot \frac{15 x^{2}}{x + 2}$

Step 1.2

Factor $2$ out of $4$ .

$\frac{2 x + 2 \cdot 2}{10 x} \cdot \frac{15 x^{2}}{x + 2}$

Step 1.3

Factor $2$ out of $2 x + 2 \cdot 2$ .

$\frac{2 (x + 2)}{10 x} \cdot \frac{15 x^{2}}{x + 2}$

Step 2

Cancel the common factor of $x + 2$ .

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Step 2.1

Factor $x + 2$ out of $2 (x + 2)$ .

$\frac{(x + 2) \cdot 2}{10 x} \cdot \frac{15 x^{2}}{x + 2}$

Step 2.2

Cancel the common factor.

$\frac{(x + 2) \cdot 2}{10 x} \cdot \frac{15 x^{2}}{x + 2}$

Step 2.3

Rewrite the expression.

$\frac{2}{10 x} \cdot (15 x^{2})$

Step 3

Cancel the common factor of $5 x$ .

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Step 3.1

Factor $5 x$ out of $10 x$ .

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

Step 3.2

Factor $5 x$ out of $15 x^{2}$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

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

Step 4

Combine $3$ and $\frac{2}{2}$ .

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

Step 5

Multiply $3$ by $2$ .

$\frac{6}{2} \cdot x$

Step 6

Combine $\frac{6}{2}$ and $x$ .

$\frac{6 x}{2}$

Step 7

Cancel the common factor of $6$ and $2$ .

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Step 7.1

Factor $2$ out of $6 x$ .

$\frac{2 (3 x)}{2}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $2$ .

$\frac{2 (3 x)}{2 (1)}$

Step 7.2.2

Cancel the common factor.

$\frac{2 (3 x)}{2 \cdot 1}$

Step 7.2.3

Rewrite the expression.

$\frac{3 x}{1}$

Step 7.2.4

Divide $3 x$ by $1$ .

$3 x$