Pre-Algebra Examples

$\frac{12 m^{3} - m^{2} n + 4 m n^{2} n^{3}}{- 3 m n}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $m$ out of $12 m^{3} - m^{2} n + 4 m n^{2} n^{3}$ .

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Step 1.1.1

Factor $m$ out of $12 m^{3}$ .

$\frac{m (12 m^{2}) - m^{2} n + 4 m n^{2} n^{3}}{- 3 m n}$

Step 1.1.2

Factor $m$ out of $- m^{2} n$ .

$\frac{m (12 m^{2}) + m (- m n) + 4 m n^{2} n^{3}}{- 3 m n}$

Step 1.1.3

Factor $m$ out of $4 m n^{2} n^{3}$ .

$\frac{m (12 m^{2}) + m (- m n) + m (4 n^{2} n^{3})}{- 3 m n}$

Step 1.1.4

Factor $m$ out of $m (12 m^{2}) + m (- m n)$ .

$\frac{m (12 m^{2} - m n) + m (4 n^{2} n^{3})}{- 3 m n}$

Step 1.1.5

Factor $m$ out of $m (12 m^{2} - m n) + m (4 n^{2} n^{3})$ .

$\frac{m (12 m^{2} - m n + 4 n^{2} n^{3})}{- 3 m n}$

Step 1.2

Multiply $n^{2}$ by $n^{3}$ by adding the exponents.

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Step 1.2.1

Move $n^{3}$ .

$\frac{m (12 m^{2} - m n + 4 (n^{3} n^{2}))}{- 3 m n}$

Step 1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{m (12 m^{2} - m n + 4 n^{3 + 2})}{- 3 m n}$

Step 1.2.3

Add $3$ and $2$ .

$\frac{m (12 m^{2} - m n + 4 n^{5})}{- 3 m n}$

Step 2

Cancel the common factor of $m$ .

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Step 2.1

Cancel the common factor.

$\frac{m (12 m^{2} - m n + 4 n^{5})}{- 3 m n}$

Step 2.2

Rewrite the expression.

$\frac{12 m^{2} - m n + 4 n^{5}}{- 3 n}$

Step 3

Move the negative in front of the fraction.

$- \frac{12 m^{2} - m n + 4 n^{5}}{3 n}$

Step 4

Split the fraction $\frac{12 m^{2} - m n + 4 n^{5}}{3 n}$ into two fractions.

$- (\frac{12 m^{2} - m n}{3 n} + \frac{4 n^{5}}{3 n})$

Step 5

Split the fraction $\frac{12 m^{2} - m n}{3 n}$ into two fractions.

$- (\frac{12 m^{2}}{3 n} + \frac{- m n}{3 n} + \frac{4 n^{5}}{3 n})$

Step 6

Cancel the common factor of $12$ and $3$ .

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Step 6.1

Factor $3$ out of $12 m^{2}$ .

$- (\frac{3 (4 m^{2})}{3 n} + \frac{- m n}{3 n} + \frac{4 n^{5}}{3 n})$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $3 n$ .

$- (\frac{3 (4 m^{2})}{3 (n)} + \frac{- m n}{3 n} + \frac{4 n^{5}}{3 n})$

Step 6.2.2

Cancel the common factor.

$- (\frac{3 (4 m^{2})}{3 n} + \frac{- m n}{3 n} + \frac{4 n^{5}}{3 n})$

Step 6.2.3

Rewrite the expression.

$- (\frac{4 m^{2}}{n} + \frac{- m n}{3 n} + \frac{4 n^{5}}{3 n})$

Step 7

Cancel the common factor of $n$ .

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Step 7.1

Cancel the common factor.

$- (\frac{4 m^{2}}{n} + \frac{- m n}{3 n} + \frac{4 n^{5}}{3 n})$

Step 7.2

Rewrite the expression.

$- (\frac{4 m^{2}}{n} + \frac{- m}{3} + \frac{4 n^{5}}{3 n})$

Step 8

Move the negative in front of the fraction.

$- (\frac{4 m^{2}}{n} - \frac{m}{3} + \frac{4 n^{5}}{3 n})$

Step 9

Cancel the common factor of $n^{5}$ and $n$ .

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Step 9.1

Factor $n$ out of $4 n^{5}$ .

$- (\frac{4 m^{2}}{n} - \frac{m}{3} + \frac{n (4 n^{4})}{3 n})$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $n$ out of $3 n$ .

$- (\frac{4 m^{2}}{n} - \frac{m}{3} + \frac{n (4 n^{4})}{n \cdot 3})$

Step 9.2.2

Cancel the common factor.

$- (\frac{4 m^{2}}{n} - \frac{m}{3} + \frac{n (4 n^{4})}{n \cdot 3})$

Step 9.2.3

Rewrite the expression.

$- (\frac{4 m^{2}}{n} - \frac{m}{3} + \frac{4 n^{4}}{3})$