Pre-Algebra Examples

$\frac{- 11 u^{6} x^{5} + 18 u^{4} x^{5}}{- 2 u^{5} x^{4}}$

Step 1

Factor $u^{4} x^{5}$ out of $- 11 u^{6} x^{5} + 18 u^{4} x^{5}$ .

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Step 1.1

Factor $u^{4} x^{5}$ out of $- 11 u^{6} x^{5}$ .

$\frac{u^{4} x^{5} (- 11 u^{2}) + 18 u^{4} x^{5}}{- 2 u^{5} x^{4}}$

Step 1.2

Factor $u^{4} x^{5}$ out of $18 u^{4} x^{5}$ .

$\frac{u^{4} x^{5} (- 11 u^{2}) + u^{4} x^{5} (18)}{- 2 u^{5} x^{4}}$

Step 1.3

Factor $u^{4} x^{5}$ out of $u^{4} x^{5} (- 11 u^{2}) + u^{4} x^{5} (18)$ .

$\frac{u^{4} x^{5} (- 11 u^{2} + 18)}{- 2 u^{5} x^{4}}$

Step 2

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

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Step 2.1

Factor $u^{4}$ out of $u^{4} x^{5} (- 11 u^{2} + 18)$ .

$\frac{u^{4} (x^{5} (- 11 u^{2} + 18))}{- 2 u^{5} x^{4}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{u^{4} (x^{5} (- 11 u^{2} + 18))}{u^{4} (- 2 u x^{4})}$

Step 2.2.2

Cancel the common factor.

$\frac{u^{4} (x^{5} (- 11 u^{2} + 18))}{u^{4} (- 2 u x^{4})}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{5} (- 11 u^{2} + 18)}{- 2 u x^{4}}$

Step 3

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

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Step 3.1

Factor $x^{4}$ out of $x^{5} (- 11 u^{2} + 18)$ .

$\frac{x^{4} (x (- 11 u^{2} + 18))}{- 2 u x^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{x^{4} (x (- 11 u^{2} + 18))}{x^{4} (- 2 u)}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{4} (x (- 11 u^{2} + 18))}{x^{4} (- 2 u)}$

Step 3.2.3

Rewrite the expression.

$\frac{x (- 11 u^{2} + 18)}{- 2 u}$

Step 4

Move the negative in front of the fraction.

$- \frac{x (- 11 u^{2} + 18)}{2 u}$

Step 5

Factor $- 1$ out of $- 11 u^{2}$ .

$- \frac{x (- (11 u^{2}) + 18)}{2 u}$

Step 6

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

$- \frac{x (- (11 u^{2}) - 1 (- 18))}{2 u}$

Step 7

Factor $- 1$ out of $- (11 u^{2}) - 1 (- 18)$ .

$- \frac{x (- (11 u^{2} - 18))}{2 u}$

Step 8

Rewrite $- (11 u^{2} - 18)$ as $- 1 (11 u^{2} - 18)$ .

$- \frac{x (- 1 (11 u^{2} - 18))}{2 u}$

Step 9

Move the negative in front of the fraction.

$- - \frac{x (11 u^{2} - 18)}{2 u}$

Step 10

Multiply $- 1$ by $- 1$ .

$1 \frac{x (11 u^{2} - 18)}{2 u}$

Step 11

Multiply $\frac{x (11 u^{2} - 18)}{2 u}$ by $1$ .

$\frac{x (11 u^{2} - 18)}{2 u}$

Step 12

Apply the distributive property.

$\frac{x (11 u^{2}) + x \cdot - 18}{2 u}$

Step 13

Rewrite using the commutative property of multiplication.

$\frac{11 x u^{2} + x \cdot - 18}{2 u}$

Step 14

Move $- 18$ to the left of $x$ .

$\frac{11 x u^{2} - 18 x}{2 u}$

Step 15

Split the fraction $\frac{11 x u^{2} - 18 x}{2 u}$ into two fractions.

$\frac{11 x u^{2}}{2 u} + \frac{- 18 x}{2 u}$

Step 16

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

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Step 16.1

Factor $u$ out of $11 x u^{2}$ .

$\frac{u (11 x u)}{2 u} + \frac{- 18 x}{2 u}$

Step 16.2

Cancel the common factors.

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Step 16.2.1

Factor $u$ out of $2 u$ .

$\frac{u (11 x u)}{u \cdot 2} + \frac{- 18 x}{2 u}$

Step 16.2.2

Cancel the common factor.

$\frac{u (11 x u)}{u \cdot 2} + \frac{- 18 x}{2 u}$

Step 16.2.3

Rewrite the expression.

$\frac{11 x u}{2} + \frac{- 18 x}{2 u}$

Step 17

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

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Step 17.1

Factor $2$ out of $- 18 x$ .

$\frac{11 x u}{2} + \frac{2 (- 9 x)}{2 u}$

Step 17.2

Cancel the common factors.

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Step 17.2.1

Factor $2$ out of $2 u$ .

$\frac{11 x u}{2} + \frac{2 (- 9 x)}{2 (u)}$

Step 17.2.2

Cancel the common factor.

$\frac{11 x u}{2} + \frac{2 (- 9 x)}{2 u}$

Step 17.2.3

Rewrite the expression.

$\frac{11 x u}{2} + \frac{- 9 x}{u}$

Step 18

Move the negative in front of the fraction.

$\frac{11 x u}{2} - \frac{9 x}{u}$