Pre-Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Factor $m n^{2}$ out of $- 3 m^{3} n^{5} - m^{2} n^{2} - m n^{3}$ .

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Step 1.1.1

Factor $m n^{2}$ out of $- 3 m^{3} n^{5}$ .

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

Step 1.1.2

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

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

Step 1.1.3

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

$\frac{m n^{2} (- 3 m^{2} n^{3}) + m n^{2} (- m) + m n^{2} (- 1 n)}{- m^{2} n^{2}}$

Step 1.1.4

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

$\frac{m n^{2} (- 3 m^{2} n^{3} - m) + m n^{2} (- 1 n)}{- m^{2} n^{2}}$

Step 1.1.5

Factor $m n^{2}$ out of $m n^{2} (- 3 m^{2} n^{3} - m) + m n^{2} (- 1 n)$ .

$\frac{m n^{2} (- 3 m^{2} n^{3} - m - 1 n)}{- m^{2} n^{2}}$

Step 1.2

Rewrite $- 1 n$ as $- n$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $n^{2}$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\frac{- 3 m^{2} n^{3} - m - n}{- m}$

Step 4

Move the negative in front of the fraction.

$- \frac{- 3 m^{2} n^{3} - m - n}{m}$

Step 5

Factor $- 1$ out of $- 3 m^{2} n^{3}$ .

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

Step 6

Factor $- 1$ out of $- m$ .

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

Step 7

Factor $- 1$ out of $- (3 m^{2} n^{3}) - (m)$ .

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

Step 8

Factor $- 1$ out of $- n$ .

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

Step 9

Factor $- 1$ out of $- (3 m^{2} n^{3} + m) - (n)$ .

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

Step 10

Rewrite $- (3 m^{2} n^{3} + m + n)$ as $- 1 (3 m^{2} n^{3} + m + n)$ .

$- \frac{- 1 (3 m^{2} n^{3} + m + n)}{m}$

Step 11

Move the negative in front of the fraction.

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

Step 12

Multiply $- 1$ by $- 1$ .

$1 \frac{3 m^{2} n^{3} + m + n}{m}$

Step 13

Multiply $\frac{3 m^{2} n^{3} + m + n}{m}$ by $1$ .

$\frac{3 m^{2} n^{3} + m + n}{m}$

Step 14

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

$\frac{3 m^{2} n^{3} + m}{m} + \frac{n}{m}$

Step 15

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

$\frac{3 m^{2} n^{3}}{m} + \frac{m}{m} + \frac{n}{m}$

Step 16

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

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Step 16.1

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

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

Step 16.2

Cancel the common factors.

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Step 16.2.1

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

$\frac{m (3 m n^{3})}{m^{1}} + \frac{m}{m} + \frac{n}{m}$

Step 16.2.2

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

$\frac{m (3 m n^{3})}{m \cdot 1} + \frac{m}{m} + \frac{n}{m}$

Step 16.2.3

Cancel the common factor.

$\frac{m (3 m n^{3})}{m \cdot 1} + \frac{m}{m} + \frac{n}{m}$

Step 16.2.4

Rewrite the expression.

$\frac{3 m n^{3}}{1} + \frac{m}{m} + \frac{n}{m}$

Step 16.2.5

Divide $3 m n^{3}$ by $1$ .

$3 m n^{3} + \frac{m}{m} + \frac{n}{m}$

Step 17

Cancel the common factor of $m$ .

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Step 17.1

Cancel the common factor.

$3 m n^{3} + \frac{m}{m} + \frac{n}{m}$

Step 17.2

Rewrite the expression.

$3 m n^{3} + 1 + \frac{n}{m}$