Pre-Algebra Examples

$(- 29 x^{5} u^{3} + 20 x^{5} u^{7}) \div (- 4 x^{4} u^{5})$

Step 1

Rewrite the division as a fraction.

$\frac{- 29 x^{5} u^{3} + 20 x^{5} u^{7}}{- 4 x^{4} u^{5}}$

Step 2

Factor $x^{5} u^{3}$ out of $- 29 x^{5} u^{3} + 20 x^{5} u^{7}$ .

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Step 2.1

Factor $x^{5} u^{3}$ out of $- 29 x^{5} u^{3}$ .

$\frac{x^{5} u^{3} (- 29) + 20 x^{5} u^{7}}{- 4 x^{4} u^{5}}$

Step 2.2

Factor $x^{5} u^{3}$ out of $20 x^{5} u^{7}$ .

$\frac{x^{5} u^{3} (- 29) + x^{5} u^{3} (20 u^{4})}{- 4 x^{4} u^{5}}$

Step 2.3

Factor $x^{5} u^{3}$ out of $x^{5} u^{3} (- 29) + x^{5} u^{3} (20 u^{4})$ .

$\frac{x^{5} u^{3} (- 29 + 20 u^{4})}{- 4 x^{4} u^{5}}$

Step 3

Cancel the common factor of $x^{5}$ and $x^{4}$ .

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Step 3.1

Factor $x^{4}$ out of $x^{5} u^{3} (- 29 + 20 u^{4})$ .

$\frac{x^{4} (x u^{3} (- 29 + 20 u^{4}))}{- 4 x^{4} u^{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{4}$ out of $- 4 x^{4} u^{5}$ .

$\frac{x^{4} (x u^{3} (- 29 + 20 u^{4}))}{x^{4} (- 4 u^{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{4} (x u^{3} (- 29 + 20 u^{4}))}{x^{4} (- 4 u^{5})}$

Step 3.2.3

Rewrite the expression.

$\frac{x u^{3} (- 29 + 20 u^{4})}{- 4 u^{5}}$

Step 4

Cancel the common factor of $u^{3}$ and $u^{5}$ .

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Step 4.1

Factor $u^{3}$ out of $x u^{3} (- 29 + 20 u^{4})$ .

$\frac{u^{3} (x (- 29 + 20 u^{4}))}{- 4 u^{5}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\frac{u^{3} (x (- 29 + 20 u^{4}))}{u^{3} (- 4 u^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{u^{3} (x (- 29 + 20 u^{4}))}{u^{3} (- 4 u^{2})}$

Step 4.2.3

Rewrite the expression.

$\frac{x (- 29 + 20 u^{4})}{- 4 u^{2}}$

Step 5

Move the negative in front of the fraction.

$- \frac{x (- 29 + 20 u^{4})}{4 u^{2}}$

Step 6

Rewrite $- 29$ as $- 1 (29)$ .

$- \frac{x (- 1 (29) + 20 u^{4})}{4 u^{2}}$

Step 7

Factor $- 1$ out of $20 u^{4}$ .

$- \frac{x (- 1 (29) - (- 20 u^{4}))}{4 u^{2}}$

Step 8

Factor $- 1$ out of $- 1 (29) - (- 20 u^{4})$ .

$- \frac{x (- 1 (29 - 20 u^{4}))}{4 u^{2}}$

Step 9

Move the negative in front of the fraction.

$- - \frac{x (29 - 20 u^{4})}{4 u^{2}}$

Step 10

Multiply $- 1$ by $- 1$ .

$1 \frac{x (29 - 20 u^{4})}{4 u^{2}}$

Step 11

Multiply $\frac{x (29 - 20 u^{4})}{4 u^{2}}$ by $1$ .

$\frac{x (29 - 20 u^{4})}{4 u^{2}}$

Step 12

Apply the distributive property.

$\frac{x \cdot 29 + x (- 20 u^{4})}{4 u^{2}}$

Step 13

Move $29$ to the left of $x$ .

$\frac{29 \cdot x + x (- 20 u^{4})}{4 u^{2}}$

Step 14

Rewrite using the commutative property of multiplication.

$\frac{29 x - 20 x u^{4}}{4 u^{2}}$

Step 15

Split the fraction $\frac{29 x - 20 x u^{4}}{4 u^{2}}$ into two fractions.

$\frac{29 x}{4 u^{2}} + \frac{- 20 x u^{4}}{4 u^{2}}$

Step 16

Cancel the common factor of $- 20$ and $4$ .

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Step 16.1

Factor $4$ out of $- 20 x u^{4}$ .

$\frac{29 x}{4 u^{2}} + \frac{4 (- 5 x u^{4})}{4 u^{2}}$

Step 16.2

Cancel the common factors.

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Step 16.2.1

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

$\frac{29 x}{4 u^{2}} + \frac{4 (- 5 x u^{4})}{4 (u^{2})}$

Step 16.2.2

Cancel the common factor.

$\frac{29 x}{4 u^{2}} + \frac{4 (- 5 x u^{4})}{4 u^{2}}$

Step 16.2.3

Rewrite the expression.

$\frac{29 x}{4 u^{2}} + \frac{- 5 x u^{4}}{u^{2}}$

Step 17

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

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Step 17.1

Factor $u^{2}$ out of $- 5 x u^{4}$ .

$\frac{29 x}{4 u^{2}} + \frac{u^{2} (- 5 x u^{2})}{u^{2}}$

Step 17.2

Cancel the common factors.

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Step 17.2.1

Multiply by $1$ .

$\frac{29 x}{4 u^{2}} + \frac{u^{2} (- 5 x u^{2})}{u^{2} \cdot 1}$

Step 17.2.2

Cancel the common factor.

$\frac{29 x}{4 u^{2}} + \frac{u^{2} (- 5 x u^{2})}{u^{2} \cdot 1}$

Step 17.2.3

Rewrite the expression.

$\frac{29 x}{4 u^{2}} + \frac{- 5 x u^{2}}{1}$

Step 17.2.4

Divide $- 5 x u^{2}$ by $1$ .

$\frac{29 x}{4 u^{2}} - 5 x u^{2}$