Pre-Algebra Examples

$\frac{- 12 a^{3} + 36 a - 15}{3 a}$

Step 1

Cancel the common factor of $- 12 a^{3} + 36 a - 15$ and $3$ .

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Step 1.1

Factor $3$ out of $- 12 a^{3}$ .

$\frac{3 (- 4 a^{3}) + 36 a - 15}{3 a}$

Step 1.2

Factor $3$ out of $36 a$ .

$\frac{3 (- 4 a^{3}) + 3 (12 a) - 15}{3 a}$

Step 1.3

Factor $3$ out of $3 (- 4 a^{3}) + 3 (12 a)$ .

$\frac{3 (- 4 a^{3} + 12 a) - 15}{3 a}$

Step 1.4

Factor $3$ out of $- 15$ .

$\frac{3 (- 4 a^{3} + 12 a) + 3 \cdot - 5}{3 a}$

Step 1.5

Factor $3$ out of $3 (- 4 a^{3} + 12 a) + 3 (- 5)$ .

$\frac{3 (- 4 a^{3} + 12 a - 5)}{3 a}$

Step 1.6

Cancel the common factors.

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Step 1.6.1

Factor $3$ out of $3 a$ .

$\frac{3 (- 4 a^{3} + 12 a - 5)}{3 (a)}$

Step 1.6.2

Cancel the common factor.

$\frac{3 (- 4 a^{3} + 12 a - 5)}{3 a}$

Step 1.6.3

Rewrite the expression.

$\frac{- 4 a^{3} + 12 a - 5}{a}$

Step 2

Factor $- 1$ out of $- 4 a^{3}$ .

$\frac{- (4 a^{3}) + 12 a - 5}{a}$

Step 3

Factor $- 1$ out of $12 a$ .

$\frac{- (4 a^{3}) - (- 12 a) - 5}{a}$

Step 4

Factor $- 1$ out of $- (4 a^{3}) - (- 12 a)$ .

$\frac{- (4 a^{3} - 12 a) - 5}{a}$

Step 5

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- (4 a^{3} - 12 a) - 1 (5)}{a}$

Step 6

Factor $- 1$ out of $- (4 a^{3} - 12 a) - 1 (5)$ .

$\frac{- (4 a^{3} - 12 a + 5)}{a}$

Step 7

Rewrite $- (4 a^{3} - 12 a + 5)$ as $- 1 (4 a^{3} - 12 a + 5)$ .

$\frac{- 1 (4 a^{3} - 12 a + 5)}{a}$

Step 8

Move the negative in front of the fraction.

$- \frac{4 a^{3} - 12 a + 5}{a}$

Step 9

Split the fraction $\frac{4 a^{3} - 12 a + 5}{a}$ into two fractions.

$- (\frac{4 a^{3} - 12 a}{a} + \frac{5}{a})$

Step 10

Split the fraction $\frac{4 a^{3} - 12 a}{a}$ into two fractions.

$- (\frac{4 a^{3}}{a} + \frac{- 12 a}{a} + \frac{5}{a})$

Step 11

Cancel the common factor of $a^{3}$ and $a$ .

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Step 11.1

Factor $a$ out of $4 a^{3}$ .

$- (\frac{a (4 a^{2})}{a} + \frac{- 12 a}{a} + \frac{5}{a})$

Step 11.2

Cancel the common factors.

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Step 11.2.1

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

$- (\frac{a (4 a^{2})}{a^{1}} + \frac{- 12 a}{a} + \frac{5}{a})$

Step 11.2.2

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

$- (\frac{a (4 a^{2})}{a \cdot 1} + \frac{- 12 a}{a} + \frac{5}{a})$

Step 11.2.3

Cancel the common factor.

$- (\frac{a (4 a^{2})}{a \cdot 1} + \frac{- 12 a}{a} + \frac{5}{a})$

Step 11.2.4

Rewrite the expression.

$- (\frac{4 a^{2}}{1} + \frac{- 12 a}{a} + \frac{5}{a})$

Step 11.2.5

Divide $4 a^{2}$ by $1$ .

$- (4 a^{2} + \frac{- 12 a}{a} + \frac{5}{a})$

Step 12

Cancel the common factor of $a$ .

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Step 12.1

Cancel the common factor.

$- (4 a^{2} + \frac{- 12 a}{a} + \frac{5}{a})$

Step 12.2

Divide $- 12$ by $1$ .

$- (4 a^{2} - 12 + \frac{5}{a})$