Pre-Algebra Examples

$\frac{- 8 u^{5} y^{6} + 12 u^{4} y^{7} - 36 u y^{3}}{4 u^{3} y^{5}}$

Step 1

Factor $4 u y^{3}$ out of $- 8 u^{5} y^{6} + 12 u^{4} y^{7} - 36 u y^{3}$ .

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Step 1.1

Factor $4 u y^{3}$ out of $- 8 u^{5} y^{6}$ .

$\frac{4 u y^{3} (- 2 u^{4} y^{3}) + 12 u^{4} y^{7} - 36 u y^{3}}{4 u^{3} y^{5}}$

Step 1.2

Factor $4 u y^{3}$ out of $12 u^{4} y^{7}$ .

$\frac{4 u y^{3} (- 2 u^{4} y^{3}) + 4 u y^{3} (3 u^{3} y^{4}) - 36 u y^{3}}{4 u^{3} y^{5}}$

Step 1.3

Factor $4 u y^{3}$ out of $- 36 u y^{3}$ .

$\frac{4 u y^{3} (- 2 u^{4} y^{3}) + 4 u y^{3} (3 u^{3} y^{4}) + 4 u y^{3} (- 9)}{4 u^{3} y^{5}}$

Step 1.4

Factor $4 u y^{3}$ out of $4 u y^{3} (- 2 u^{4} y^{3}) + 4 u y^{3} (3 u^{3} y^{4})$ .

$\frac{4 u y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4}) + 4 u y^{3} (- 9)}{4 u^{3} y^{5}}$

Step 1.5

Factor $4 u y^{3}$ out of $4 u y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4}) + 4 u y^{3} (- 9)$ .

$\frac{4 u y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9)}{4 u^{3} y^{5}}$

Step 2

Cancel the common factor of $4$ .

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Step 2.1

Cancel the common factor.

$\frac{4 u y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9)}{4 u^{3} y^{5}}$

Step 2.2

Rewrite the expression.

$\frac{u y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9)}{u^{3} y^{5}}$

Step 3

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

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Step 3.1

Factor $u$ out of $u y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9)$ .

$\frac{u (y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9))}{u^{3} y^{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $u$ out of $u^{3} y^{5}$ .

$\frac{u (y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9))}{u (u^{2} y^{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{u (y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9))}{u (u^{2} y^{5})}$

Step 3.2.3

Rewrite the expression.

$\frac{y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9)}{u^{2} y^{5}}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $y^{3}$ out of $u^{2} y^{5}$ .

$\frac{y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9)}{y^{3} (u^{2} y^{2})}$

Step 4.2

Cancel the common factor.

$\frac{y^{3} (- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9)}{y^{3} (u^{2} y^{2})}$

Step 4.3

Rewrite the expression.

$\frac{- 2 u^{4} y^{3} + 3 u^{3} y^{4} - 9}{u^{2} y^{2}}$

Step 5

Factor $- 1$ out of $- 2 u^{4} y^{3}$ .

$\frac{- (2 u^{4} y^{3}) + 3 u^{3} y^{4} - 9}{u^{2} y^{2}}$

Step 6

Factor $- 1$ out of $3 u^{3} y^{4}$ .

$\frac{- (2 u^{4} y^{3}) - (- 3 u^{3} y^{4}) - 9}{u^{2} y^{2}}$

Step 7

Factor $- 1$ out of $- (2 u^{4} y^{3}) - (- 3 u^{3} y^{4})$ .

$\frac{- (2 u^{4} y^{3} - 3 u^{3} y^{4}) - 9}{u^{2} y^{2}}$

Step 8

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- (2 u^{4} y^{3} - 3 u^{3} y^{4}) - 1 (9)}{u^{2} y^{2}}$

Step 9

Factor $- 1$ out of $- (2 u^{4} y^{3} - 3 u^{3} y^{4}) - 1 (9)$ .

$\frac{- (2 u^{4} y^{3} - 3 u^{3} y^{4} + 9)}{u^{2} y^{2}}$

Step 10

Rewrite $- (2 u^{4} y^{3} - 3 u^{3} y^{4} + 9)$ as $- 1 (2 u^{4} y^{3} - 3 u^{3} y^{4} + 9)$ .

$\frac{- 1 (2 u^{4} y^{3} - 3 u^{3} y^{4} + 9)}{u^{2} y^{2}}$

Step 11

Move the negative in front of the fraction.

$- \frac{2 u^{4} y^{3} - 3 u^{3} y^{4} + 9}{u^{2} y^{2}}$

Step 12

Split the fraction $\frac{2 u^{4} y^{3} - 3 u^{3} y^{4} + 9}{u^{2} y^{2}}$ into two fractions.

$- (\frac{2 u^{4} y^{3} - 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 13

Split the fraction $\frac{2 u^{4} y^{3} - 3 u^{3} y^{4}}{u^{2} y^{2}}$ into two fractions.

$- (\frac{2 u^{4} y^{3}}{u^{2} y^{2}} + \frac{- 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 14

Cancel the common factor of $u^{4}$ and $u^{2}$ .

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Step 14.1

Factor $u^{2}$ out of $2 u^{4} y^{3}$ .

$- (\frac{u^{2} (2 u^{2} y^{3})}{u^{2} y^{2}} + \frac{- 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 14.2

Cancel the common factors.

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Step 14.2.1

Factor $u^{2}$ out of $u^{2} y^{2}$ .

$- (\frac{u^{2} (2 u^{2} y^{3})}{u^{2} (y^{2})} + \frac{- 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 14.2.2

Cancel the common factor.

$- (\frac{u^{2} (2 u^{2} y^{3})}{u^{2} y^{2}} + \frac{- 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 14.2.3

Rewrite the expression.

$- (\frac{2 u^{2} y^{3}}{y^{2}} + \frac{- 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 15

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

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Step 15.1

Factor $y^{2}$ out of $2 u^{2} y^{3}$ .

$- (\frac{y^{2} (2 u^{2} y)}{y^{2}} + \frac{- 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 15.2

Cancel the common factors.

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Step 15.2.1

Multiply by $1$ .

$- (\frac{y^{2} (2 u^{2} y)}{y^{2} \cdot 1} + \frac{- 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 15.2.2

Cancel the common factor.

$- (\frac{y^{2} (2 u^{2} y)}{y^{2} \cdot 1} + \frac{- 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 15.2.3

Rewrite the expression.

$- (\frac{2 u^{2} y}{1} + \frac{- 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 15.2.4

Divide $2 u^{2} y$ by $1$ .

$- (2 u^{2} y + \frac{- 3 u^{3} y^{4}}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 16

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

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Step 16.1

Factor $u^{2}$ out of $- 3 u^{3} y^{4}$ .

$- (2 u^{2} y + \frac{u^{2} (- 3 u y^{4})}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 16.2

Cancel the common factors.

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Step 16.2.1

Factor $u^{2}$ out of $u^{2} y^{2}$ .

$- (2 u^{2} y + \frac{u^{2} (- 3 u y^{4})}{u^{2} (y^{2})} + \frac{9}{u^{2} y^{2}})$

Step 16.2.2

Cancel the common factor.

$- (2 u^{2} y + \frac{u^{2} (- 3 u y^{4})}{u^{2} y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 16.2.3

Rewrite the expression.

$- (2 u^{2} y + \frac{- 3 u y^{4}}{y^{2}} + \frac{9}{u^{2} y^{2}})$

Step 17

Cancel the common factor of $y^{4}$ and $y^{2}$ .

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Step 17.1

Factor $y^{2}$ out of $- 3 u y^{4}$ .

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

Step 17.2

Cancel the common factors.

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Step 17.2.1

Multiply by $1$ .

$- (2 u^{2} y + \frac{y^{2} (- 3 u y^{2})}{y^{2} \cdot 1} + \frac{9}{u^{2} y^{2}})$

Step 17.2.2

Cancel the common factor.

$- (2 u^{2} y + \frac{y^{2} (- 3 u y^{2})}{y^{2} \cdot 1} + \frac{9}{u^{2} y^{2}})$

Step 17.2.3

Rewrite the expression.

$- (2 u^{2} y + \frac{- 3 u y^{2}}{1} + \frac{9}{u^{2} y^{2}})$

Step 17.2.4

Divide $- 3 u y^{2}$ by $1$ .

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