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Calculus Examples

$\frac{12 x^{2} + 2 x}{6 x}$

Step 1

Factor $2 x$ out of $12 x^{2} + 2 x$ .

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Step 1.1

Factor $2 x$ out of $12 x^{2}$ .

$\frac{2 x (6 x) + 2 x}{6 x}$

Step 1.2

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

$\frac{2 x (6 x) + 2 x (1)}{6 x}$

Step 1.3

Factor $2 x$ out of $2 x (6 x) + 2 x (1)$ .

$\frac{2 x (6 x + 1)}{6 x}$

$\frac{2 x (6 x + 1)}{6 x}$

Step 2

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

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Step 2.1

Factor $2$ out of $2 x (6 x + 1)$ .

$\frac{2 (x (6 x + 1))}{6 x}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $6 x$ .

$\frac{2 (x (6 x + 1))}{2 (3 x)}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (x (6 x + 1))}{2 (3 x)}$

Step 2.2.3

Rewrite the expression.

$\frac{x (6 x + 1)}{3 x}$

$\frac{x (6 x + 1)}{3 x}$

$\frac{x (6 x + 1)}{3 x}$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\frac{x (6 x + 1)}{3 x}$

Step 3.2

Rewrite the expression.

$\frac{6 x + 1}{3}$

$\frac{6 x + 1}{3}$

Step 4

Split the fraction $\frac{6 x + 1}{3}$ into two fractions.

$\frac{6 x}{3} + \frac{1}{3}$

Step 5

Cancel the common factor of $6$ and $3$ .

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Step 5.1

Factor $3$ out of $6 x$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $3$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{2 x}{1} + \frac{1}{3}$

Step 5.2.4

Divide $2 x$ by $1$ .

$2 x + \frac{1}{3}$

$2 x + \frac{1}{3}$

$2 x + \frac{1}{3}$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$