Algebra Examples

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

Step 1

Factor $x$ out of $x^{2} + x$ .

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Step 1.1

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

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

Step 1.2

Raise $x$ to the power of $1$ .

$\frac{2}{x \cdot x + x^{1}} \cdot \frac{2 x + 2}{x}$

Step 1.3

Factor $x$ out of $x^{1}$ .

$\frac{2}{x \cdot x + x \cdot 1} \cdot \frac{2 x + 2}{x}$

Step 1.4

Factor $x$ out of $x \cdot x + x \cdot 1$ .

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

Step 2

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

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Step 2.1

Factor $2$ out of $2 x$ .

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

Step 2.2

Factor $2$ out of $2$ .

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

Step 2.3

Factor $2$ out of $2 (x) + 2 (1)$ .

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

Step 3

Cancel the common factor of $x + 1$ .

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Step 3.1

Factor $x + 1$ out of $x (x + 1)$ .

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

Step 3.2

Factor $x + 1$ out of $2 (x + 1)$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

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

Step 4

Multiply $\frac{2}{x}$ by $\frac{2}{x}$ .

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

Step 5

Multiply $2$ by $2$ .

$\frac{4}{x \cdot x}$

Step 6

Raise $x$ to the power of $1$ .

$\frac{4}{x^{1} x}$

Step 7

Raise $x$ to the power of $1$ .

$\frac{4}{x^{1} x^{1}}$

Step 8

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{x^{1 + 1}}$

Step 9

Add $1$ and $1$ .

$\frac{4}{x^{2}}$