Pre-Algebra Examples

$\frac{- 18 y u^{5} + 5 y^{7} u^{5}}{- 2 y^{2} u^{4}}$

Step 1

Factor $y u^{5}$ out of $- 18 y u^{5} + 5 y^{7} u^{5}$ .

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Step 1.1

Factor $y u^{5}$ out of $- 18 y u^{5}$ .

$\frac{y u^{5} (- 18) + 5 y^{7} u^{5}}{- 2 y^{2} u^{4}}$

Step 1.2

Factor $y u^{5}$ out of $5 y^{7} u^{5}$ .

$\frac{y u^{5} (- 18) + y u^{5} (5 y^{6})}{- 2 y^{2} u^{4}}$

Step 1.3

Factor $y u^{5}$ out of $y u^{5} (- 18) + y u^{5} (5 y^{6})$ .

$\frac{y u^{5} (- 18 + 5 y^{6})}{- 2 y^{2} u^{4}}$

Step 2

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

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Step 2.1

Factor $y$ out of $y u^{5} (- 18 + 5 y^{6})$ .

$\frac{y (u^{5} (- 18 + 5 y^{6}))}{- 2 y^{2} u^{4}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{y (u^{5} (- 18 + 5 y^{6}))}{y (- 2 y u^{4})}$

Step 2.2.2

Cancel the common factor.

$\frac{y (u^{5} (- 18 + 5 y^{6}))}{y (- 2 y u^{4})}$

Step 2.2.3

Rewrite the expression.

$\frac{u^{5} (- 18 + 5 y^{6})}{- 2 y u^{4}}$

Step 3

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

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Step 3.1

Factor $u^{4}$ out of $u^{5} (- 18 + 5 y^{6})$ .

$\frac{u^{4} (u (- 18 + 5 y^{6}))}{- 2 y u^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{u^{4} (u (- 18 + 5 y^{6}))}{u^{4} (- 2 y)}$

Step 3.2.2

Cancel the common factor.

$\frac{u^{4} (u (- 18 + 5 y^{6}))}{u^{4} (- 2 y)}$

Step 3.2.3

Rewrite the expression.

$\frac{u (- 18 + 5 y^{6})}{- 2 y}$

Step 4

Move the negative in front of the fraction.

$- \frac{u (- 18 + 5 y^{6})}{2 y}$

Step 5

Rewrite $- 18$ as $- 1 (18)$ .

$- \frac{u (- 1 (18) + 5 y^{6})}{2 y}$

Step 6

Factor $- 1$ out of $5 y^{6}$ .

$- \frac{u (- 1 (18) - (- 5 y^{6}))}{2 y}$

Step 7

Factor $- 1$ out of $- 1 (18) - (- 5 y^{6})$ .

$- \frac{u (- 1 (18 - 5 y^{6}))}{2 y}$

Step 8

Move the negative in front of the fraction.

$- - \frac{u (18 - 5 y^{6})}{2 y}$

Step 9

Multiply $- 1$ by $- 1$ .

$1 \frac{u (18 - 5 y^{6})}{2 y}$

Step 10

Multiply $\frac{u (18 - 5 y^{6})}{2 y}$ by $1$ .

$\frac{u (18 - 5 y^{6})}{2 y}$

Step 11

Apply the distributive property.

$\frac{u \cdot 18 + u (- 5 y^{6})}{2 y}$

Step 12

Move $18$ to the left of $u$ .

$\frac{18 \cdot u + u (- 5 y^{6})}{2 y}$

Step 13

Rewrite using the commutative property of multiplication.

$\frac{18 u - 5 u y^{6}}{2 y}$

Step 14

Split the fraction $\frac{18 u - 5 u y^{6}}{2 y}$ into two fractions.

$\frac{18 u}{2 y} + \frac{- 5 u y^{6}}{2 y}$

Step 15

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

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Step 15.1

Factor $2$ out of $18 u$ .

$\frac{2 (9 u)}{2 y} + \frac{- 5 u y^{6}}{2 y}$

Step 15.2

Cancel the common factors.

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Step 15.2.1

Factor $2$ out of $2 y$ .

$\frac{2 (9 u)}{2 (y)} + \frac{- 5 u y^{6}}{2 y}$

Step 15.2.2

Cancel the common factor.

$\frac{2 (9 u)}{2 y} + \frac{- 5 u y^{6}}{2 y}$

Step 15.2.3

Rewrite the expression.

$\frac{9 u}{y} + \frac{- 5 u y^{6}}{2 y}$

Step 16

Cancel the common factor of $y^{6}$ and $y$ .

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Step 16.1

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

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

Step 16.2

Cancel the common factors.

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Step 16.2.1

Factor $y$ out of $2 y$ .

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

Step 16.2.2

Cancel the common factor.

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

Step 16.2.3

Rewrite the expression.

$\frac{9 u}{y} + \frac{- 5 u y^{5}}{2}$

Step 17

Move the negative in front of the fraction.

$\frac{9 u}{y} - \frac{5 u y^{5}}{2}$