Pre-Algebra Examples

$\frac{18 a^{3} - 15 a^{2} - 6 a}{3 a^{2}}$

Step 1

Factor $3 a$ out of $18 a^{3} - 15 a^{2} - 6 a$ .

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Step 1.1

Factor $3 a$ out of $18 a^{3}$ .

$\frac{3 a (6 a^{2}) - 15 a^{2} - 6 a}{3 a^{2}}$

Step 1.2

Factor $3 a$ out of $- 15 a^{2}$ .

$\frac{3 a (6 a^{2}) + 3 a (- 5 a) - 6 a}{3 a^{2}}$

Step 1.3

Factor $3 a$ out of $- 6 a$ .

$\frac{3 a (6 a^{2}) + 3 a (- 5 a) + 3 a (- 2)}{3 a^{2}}$

Step 1.4

Factor $3 a$ out of $3 a (6 a^{2}) + 3 a (- 5 a)$ .

$\frac{3 a (6 a^{2} - 5 a) + 3 a (- 2)}{3 a^{2}}$

Step 1.5

Factor $3 a$ out of $3 a (6 a^{2} - 5 a) + 3 a (- 2)$ .

$\frac{3 a (6 a^{2} - 5 a - 2)}{3 a^{2}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{3 a (6 a^{2} - 5 a - 2)}{3 a^{2}}$

Step 2.2

Rewrite the expression.

$\frac{a (6 a^{2} - 5 a - 2)}{a^{2}}$

Step 3

Cancel the common factors.

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Step 3.1

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

$\frac{a (6 a^{2} - 5 a - 2)}{a \cdot a}$

Step 3.2

Cancel the common factor.

$\frac{a (6 a^{2} - 5 a - 2)}{a \cdot a}$

Step 3.3

Rewrite the expression.

$\frac{6 a^{2} - 5 a - 2}{a}$

Step 4

Split the fraction $\frac{6 a^{2} - 5 a - 2}{a}$ into two fractions.

$\frac{6 a^{2} - 5 a}{a} + \frac{- 2}{a}$

Step 5

Split the fraction $\frac{6 a^{2} - 5 a}{a}$ into two fractions.

$\frac{6 a^{2}}{a} + \frac{- 5 a}{a} + \frac{- 2}{a}$

Step 6

Cancel the common factor of $a^{2}$ and $a$ .

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Step 6.1

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

$\frac{a (6 a)}{a} + \frac{- 5 a}{a} + \frac{- 2}{a}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

$\frac{a (6 a)}{a^{1}} + \frac{- 5 a}{a} + \frac{- 2}{a}$

Step 6.2.2

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

$\frac{a (6 a)}{a \cdot 1} + \frac{- 5 a}{a} + \frac{- 2}{a}$

Step 6.2.3

Cancel the common factor.

$\frac{a (6 a)}{a \cdot 1} + \frac{- 5 a}{a} + \frac{- 2}{a}$

Step 6.2.4

Rewrite the expression.

$\frac{6 a}{1} + \frac{- 5 a}{a} + \frac{- 2}{a}$

Step 6.2.5

Divide $6 a$ by $1$ .

$6 a + \frac{- 5 a}{a} + \frac{- 2}{a}$

Step 7

Cancel the common factor of $a$ .

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Step 7.1

Cancel the common factor.

$6 a + \frac{- 5 a}{a} + \frac{- 2}{a}$

Step 7.2

Divide $- 5$ by $1$ .

$6 a - 5 + \frac{- 2}{a}$

Step 8

Move the negative in front of the fraction.

$6 a - 5 - \frac{2}{a}$