Calculus Examples

$\frac{(14 a^{10} - 8 a^{6} + 6 a)}{20 a}$

Step 1

Factor $2 a$ out of $14 a^{10} - 8 a^{6} + 6 a$ .

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Step 1.1

Factor $2 a$ out of $14 a^{10}$ .

$\frac{2 a (7 a^{9}) - 8 a^{6} + 6 a}{20 a}$

Step 1.2

Factor $2 a$ out of $- 8 a^{6}$ .

$\frac{2 a (7 a^{9}) + 2 a (- 4 a^{5}) + 6 a}{20 a}$

Step 1.3

Factor $2 a$ out of $6 a$ .

$\frac{2 a (7 a^{9}) + 2 a (- 4 a^{5}) + 2 a (3)}{20 a}$

Step 1.4

Factor $2 a$ out of $2 a (7 a^{9}) + 2 a (- 4 a^{5})$ .

$\frac{2 a (7 a^{9} - 4 a^{5}) + 2 a (3)}{20 a}$

Step 1.5

Factor $2 a$ out of $2 a (7 a^{9} - 4 a^{5}) + 2 a (3)$ .

$\frac{2 a (7 a^{9} - 4 a^{5} + 3)}{20 a}$

Step 2

Cancel the common factor of $2$ and $20$ .

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Step 2.1

Factor $2$ out of $2 a (7 a^{9} - 4 a^{5} + 3)$ .

$\frac{2 (a (7 a^{9} - 4 a^{5} + 3))}{20 a}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $20 a$ .

$\frac{2 (a (7 a^{9} - 4 a^{5} + 3))}{2 (10 a)}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (a (7 a^{9} - 4 a^{5} + 3))}{2 (10 a)}$

Step 2.2.3

Rewrite the expression.

$\frac{a (7 a^{9} - 4 a^{5} + 3)}{10 a}$

Step 3

Cancel the common factor of $a$ .

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Step 3.1

Cancel the common factor.

$\frac{a (7 a^{9} - 4 a^{5} + 3)}{10 a}$

Step 3.2

Rewrite the expression.

$\frac{7 a^{9} - 4 a^{5} + 3}{10}$

Step 4

Split the fraction $\frac{7 a^{9} - 4 a^{5} + 3}{10}$ into two fractions.

$\frac{7 a^{9} - 4 a^{5}}{10} + \frac{3}{10}$

Step 5

Split the fraction $\frac{7 a^{9} - 4 a^{5}}{10}$ into two fractions.

$\frac{7 a^{9}}{10} + \frac{- 4 a^{5}}{10} + \frac{3}{10}$

Step 6

Cancel the common factor of $- 4$ and $10$ .

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Step 6.1

Factor $2$ out of $- 4 a^{5}$ .

$\frac{7 a^{9}}{10} + \frac{2 (- 2 a^{5})}{10} + \frac{3}{10}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $10$ .

$\frac{7 a^{9}}{10} + \frac{2 (- 2 a^{5})}{2 (5)} + \frac{3}{10}$

Step 6.2.2

Cancel the common factor.

$\frac{7 a^{9}}{10} + \frac{2 (- 2 a^{5})}{2 \cdot 5} + \frac{3}{10}$

Step 6.2.3

Rewrite the expression.

$\frac{7 a^{9}}{10} + \frac{- 2 a^{5}}{5} + \frac{3}{10}$

Step 7

Move the negative in front of the fraction.

$\frac{7 a^{9}}{10} - \frac{2 a^{5}}{5} + \frac{3}{10}$