Pre-Algebra Examples

\frac{15 a^{3} - 45 a^{2} - 40 a}{5 a^{2}}

$\frac{15 a^{3} - 45 a^{2} - 40 a}{5 a^{2}}$

Step 1

Factor

5 a

$5 a$ out of

15 a^{3} - 45 a^{2} - 40 a

$15 a^{3} - 45 a^{2} - 40 a$ .

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Step 1.1

Factor

5 a

$5 a$ out of

15 a^{3}

$15 a^{3}$ .

\frac{5 a (3 a^{2}) - 45 a^{2} - 40 a}{5 a^{2}}

$\frac{5 a (3 a^{2}) - 45 a^{2} - 40 a}{5 a^{2}}$

Step 1.2

Factor

5 a

$5 a$ out of

- 45 a^{2}

$- 45 a^{2}$ .

\frac{5 a (3 a^{2}) + 5 a (- 9 a) - 40 a}{5 a^{2}}

$\frac{5 a (3 a^{2}) + 5 a (- 9 a) - 40 a}{5 a^{2}}$

Step 1.3

Factor

5 a

$5 a$ out of

- 40 a

$- 40 a$ .

\frac{5 a (3 a^{2}) + 5 a (- 9 a) + 5 a (- 8)}{5 a^{2}}

$\frac{5 a (3 a^{2}) + 5 a (- 9 a) + 5 a (- 8)}{5 a^{2}}$

Step 1.4

Factor

5 a

$5 a$ out of

5 a (3 a^{2}) + 5 a (- 9 a)

$5 a (3 a^{2}) + 5 a (- 9 a)$ .

\frac{5 a (3 a^{2} - 9 a) + 5 a (- 8)}{5 a^{2}}

$\frac{5 a (3 a^{2} - 9 a) + 5 a (- 8)}{5 a^{2}}$

Step 1.5

Factor

5 a

$5 a$ out of

5 a (3 a^{2} - 9 a) + 5 a (- 8)

$5 a (3 a^{2} - 9 a) + 5 a (- 8)$ .

\frac{5 a (3 a^{2} - 9 a - 8)}{5 a^{2}}

$\frac{5 a (3 a^{2} - 9 a - 8)}{5 a^{2}}$

\frac{5 a (3 a^{2} - 9 a - 8)}{5 a^{2}}

$\frac{5 a (3 a^{2} - 9 a - 8)}{5 a^{2}}$

Step 2

Cancel the common factor of

5

$5$ .

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Step 2.1

Cancel the common factor.

$\frac{5 a (3 a^{2} - 9 a - 8)}{5 a^{2}}$

Step 2.2

Rewrite the expression.

$\frac{a (3 a^{2} - 9 a - 8)}{a^{2}}$

Step 3

Cancel the common factors.

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Step 3.1

Factor

$a$ out of

$a^{2}$ .

$\frac{a (3 a^{2} - 9 a - 8)}{a \cdot a}$

Step 3.2

Cancel the common factor.

$\frac{a (3 a^{2} - 9 a - 8)}{a \cdot a}$

Step 3.3

Rewrite the expression.

$\frac{3 a^{2} - 9 a - 8}{a}$

Step 4

Split the fraction

$\frac{3 a^{2} - 9 a - 8}{a}$ into two fractions.

$\frac{3 a^{2} - 9 a}{a} + \frac{- 8}{a}$

Step 5

Split the fraction

$\frac{3 a^{2} - 9 a}{a}$ into two fractions.

$\frac{3 a^{2}}{a} + \frac{- 9 a}{a} + \frac{- 8}{a}$

Step 6

Cancel the common factor of

$a^{2}$ and

$a$ .

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Step 6.1

Factor

$a$ out of

$3 a^{2}$ .

$\frac{a (3 a)}{a} + \frac{- 9 a}{a} + \frac{- 8}{a}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Raise

$a$ to the power of

$1$ .

$\frac{a (3 a)}{a^{1}} + \frac{- 9 a}{a} + \frac{- 8}{a}$

Step 6.2.2

Factor

$a$ out of

$a^{1}$ .

$\frac{a (3 a)}{a \cdot 1} + \frac{- 9 a}{a} + \frac{- 8}{a}$

Step 6.2.3

Cancel the common factor.

$\frac{a (3 a)}{a \cdot 1} + \frac{- 9 a}{a} + \frac{- 8}{a}$

Step 6.2.4

Rewrite the expression.

$\frac{3 a}{1} + \frac{- 9 a}{a} + \frac{- 8}{a}$

Step 6.2.5

Divide

$3 a$ by

$1$ .

$3 a + \frac{- 9 a}{a} + \frac{- 8}{a}$

Step 7

Cancel the common factor of

$a$ .

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Step 7.1

Cancel the common factor.

$3 a + \frac{- 9 a}{a} + \frac{- 8}{a}$

Step 7.2

Divide

$- 9$ by

$1$ .

$3 a - 9 + \frac{- 8}{a}$

Step 8

Move the negative in front of the fraction.

$3 a - 9 - \frac{8}{a}$