Pre-Algebra Examples

$(18 x u^{2} - 3 x^{2} u^{3}) \div (- 2 x^{2} u^{3})$

Step 1

Rewrite the division as a fraction.

$\frac{18 x u^{2} - 3 x^{2} u^{3}}{- 2 x^{2} u^{3}}$

Step 2

Factor $3 x u^{2}$ out of $18 x u^{2} - 3 x^{2} u^{3}$ .

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Step 2.1

Factor $3 x u^{2}$ out of $18 x u^{2}$ .

$\frac{3 x u^{2} (6) - 3 x^{2} u^{3}}{- 2 x^{2} u^{3}}$

Step 2.2

Factor $3 x u^{2}$ out of $- 3 x^{2} u^{3}$ .

$\frac{3 x u^{2} (6) + 3 x u^{2} (- x u)}{- 2 x^{2} u^{3}}$

Step 2.3

Factor $3 x u^{2}$ out of $3 x u^{2} (6) + 3 x u^{2} (- x u)$ .

$\frac{3 x u^{2} (6 - x u)}{- 2 x^{2} u^{3}}$

Step 3

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

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Step 3.1

Factor $x$ out of $3 x u^{2} (6 - x u)$ .

$\frac{x (3 u^{2} (6 - x u))}{- 2 x^{2} u^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $- 2 x^{2} u^{3}$ .

$\frac{x (3 u^{2} (6 - x u))}{x (- 2 x u^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{x (3 u^{2} (6 - x u))}{x (- 2 x u^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{3 u^{2} (6 - x u)}{- 2 x u^{3}}$

Step 4

Cancel the common factor of $u^{2}$ and $u^{3}$ .

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Step 4.1

Factor $u^{2}$ out of $3 u^{2} (6 - x u)$ .

$\frac{u^{2} (3 (6 - x u))}{- 2 x u^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $u^{2}$ out of $- 2 x u^{3}$ .

$\frac{u^{2} (3 (6 - x u))}{u^{2} (- 2 x u)}$

Step 4.2.2

Cancel the common factor.

$\frac{u^{2} (3 (6 - x u))}{u^{2} (- 2 x u)}$

Step 4.2.3

Rewrite the expression.

$\frac{3 (6 - x u)}{- 2 x u}$

Step 5

Move the negative in front of the fraction.

$- \frac{3 (6 - x u)}{2 x u}$

Step 6

Apply the distributive property.

$- \frac{3 \cdot 6 + 3 (- x u)}{2 x u}$

Step 7

Multiply $3$ by $6$ .

$- \frac{18 + 3 (- x u)}{2 x u}$

Step 8

Multiply $- 1$ by $3$ .

$- \frac{18 - 3 x u}{2 x u}$

Step 9

Split the fraction $\frac{18 - 3 x u}{2 x u}$ into two fractions.

$- (\frac{18}{2 x u} + \frac{- 3 x u}{2 x u})$

Step 10

Cancel the common factor of $18$ and $2$ .

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Step 10.1

Factor $2$ out of $18$ .

$- (\frac{2 \cdot 9}{2 x u} + \frac{- 3 x u}{2 x u})$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $2 x u$ .

$- (\frac{2 \cdot 9}{2 (x u)} + \frac{- 3 x u}{2 x u})$

Step 10.2.2

Cancel the common factor.

$- (\frac{2 \cdot 9}{2 (x u)} + \frac{- 3 x u}{2 x u})$

Step 10.2.3

Rewrite the expression.

$- (\frac{9}{x u} + \frac{- 3 x u}{2 x u})$

Step 11

Cancel the common factor of $x$ .

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Step 11.1

Cancel the common factor.

$- (\frac{9}{x u} + \frac{- 3 x u}{2 x u})$

Step 11.2

Rewrite the expression.

$- (\frac{9}{x u} + \frac{- 3 u}{2 u})$

Step 12

Cancel the common factor of $u$ .

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Step 12.1

Cancel the common factor.

$- (\frac{9}{x u} + \frac{- 3 u}{2 u})$

Step 12.2

Rewrite the expression.

$- (\frac{9}{x u} + \frac{- 3}{2})$

Step 13

Move the negative in front of the fraction.

$- (\frac{9}{x u} - \frac{3}{2})$