Pre-Algebra Examples

$\frac{- 12 v^{5} x^{2} + 16 v^{4} x^{6} + 18 v^{6} x^{6}}{2 v^{5} x^{2}}$

Step 1

Factor $2 v^{4} x^{2}$ out of $- 12 v^{5} x^{2} + 16 v^{4} x^{6} + 18 v^{6} x^{6}$ .

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Step 1.1

Factor $2 v^{4} x^{2}$ out of $- 12 v^{5} x^{2}$ .

$\frac{2 v^{4} x^{2} (- 6 v) + 16 v^{4} x^{6} + 18 v^{6} x^{6}}{2 v^{5} x^{2}}$

Step 1.2

Factor $2 v^{4} x^{2}$ out of $16 v^{4} x^{6}$ .

$\frac{2 v^{4} x^{2} (- 6 v) + 2 v^{4} x^{2} (8 x^{4}) + 18 v^{6} x^{6}}{2 v^{5} x^{2}}$

Step 1.3

Factor $2 v^{4} x^{2}$ out of $18 v^{6} x^{6}$ .

$\frac{2 v^{4} x^{2} (- 6 v) + 2 v^{4} x^{2} (8 x^{4}) + 2 v^{4} x^{2} (9 v^{2} x^{4})}{2 v^{5} x^{2}}$

Step 1.4

Factor $2 v^{4} x^{2}$ out of $2 v^{4} x^{2} (- 6 v) + 2 v^{4} x^{2} (8 x^{4})$ .

$\frac{2 v^{4} x^{2} (- 6 v + 8 x^{4}) + 2 v^{4} x^{2} (9 v^{2} x^{4})}{2 v^{5} x^{2}}$

Step 1.5

Factor $2 v^{4} x^{2}$ out of $2 v^{4} x^{2} (- 6 v + 8 x^{4}) + 2 v^{4} x^{2} (9 v^{2} x^{4})$ .

$\frac{2 v^{4} x^{2} (- 6 v + 8 x^{4} + 9 v^{2} x^{4})}{2 v^{5} x^{2}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$\frac{2 v^{4} x^{2} (- 6 v + 8 x^{4} + 9 v^{2} x^{4})}{2 v^{5} x^{2}}$

Step 2.2

Rewrite the expression.

$\frac{v^{4} x^{2} (- 6 v + 8 x^{4} + 9 v^{2} x^{4})}{v^{5} x^{2}}$

Step 3

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

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Step 3.1

Factor $v^{4}$ out of $v^{4} x^{2} (- 6 v + 8 x^{4} + 9 v^{2} x^{4})$ .

$\frac{v^{4} (x^{2} (- 6 v + 8 x^{4} + 9 v^{2} x^{4}))}{v^{5} x^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{v^{4} (x^{2} (- 6 v + 8 x^{4} + 9 v^{2} x^{4}))}{v^{4} (v x^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{v^{4} (x^{2} (- 6 v + 8 x^{4} + 9 v^{2} x^{4}))}{v^{4} (v x^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{x^{2} (- 6 v + 8 x^{4} + 9 v^{2} x^{4})}{v x^{2}}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{x^{2} (- 6 v + 8 x^{4} + 9 v^{2} x^{4})}{v x^{2}}$

Step 4.2

Rewrite the expression.

$\frac{- 6 v + 8 x^{4} + 9 v^{2} x^{4}}{v}$

Step 5

Factor $- 1$ out of $- 6 v$ .

$\frac{- (6 v) + 8 x^{4} + 9 v^{2} x^{4}}{v}$

Step 6

Factor $- 1$ out of $8 x^{4}$ .

$\frac{- (6 v) - (- 8 x^{4}) + 9 v^{2} x^{4}}{v}$

Step 7

Factor $- 1$ out of $- (6 v) - (- 8 x^{4})$ .

$\frac{- (6 v - 8 x^{4}) + 9 v^{2} x^{4}}{v}$

Step 8

Factor $- 1$ out of $9 v^{2} x^{4}$ .

$\frac{- (6 v - 8 x^{4}) - (- 9 v^{2} x^{4})}{v}$

Step 9

Factor $- 1$ out of $- (6 v - 8 x^{4}) - (- 9 v^{2} x^{4})$ .

$\frac{- (6 v - 8 x^{4} - 9 v^{2} x^{4})}{v}$

Step 10

Rewrite $- (6 v - 8 x^{4} - 9 v^{2} x^{4})$ as $- 1 (6 v - 8 x^{4} - 9 v^{2} x^{4})$ .

$\frac{- 1 (6 v - 8 x^{4} - 9 v^{2} x^{4})}{v}$

Step 11

Move the negative in front of the fraction.

$- \frac{6 v - 8 x^{4} - 9 v^{2} x^{4}}{v}$

Step 12

Split the fraction $\frac{6 v - 8 x^{4} - 9 v^{2} x^{4}}{v}$ into two fractions.

$- (\frac{6 v - 8 x^{4}}{v} + \frac{- 9 v^{2} x^{4}}{v})$

Step 13

Split the fraction $\frac{6 v - 8 x^{4}}{v}$ into two fractions.

$- (\frac{6 v}{v} + \frac{- 8 x^{4}}{v} + \frac{- 9 v^{2} x^{4}}{v})$

Step 14

Cancel the common factor of $v$ .

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Step 14.1

Cancel the common factor.

$- (\frac{6 v}{v} + \frac{- 8 x^{4}}{v} + \frac{- 9 v^{2} x^{4}}{v})$

Step 14.2

Divide $6$ by $1$ .

$- (6 + \frac{- 8 x^{4}}{v} + \frac{- 9 v^{2} x^{4}}{v})$

Step 15

Move the negative in front of the fraction.

$- (6 - \frac{8 x^{4}}{v} + \frac{- 9 v^{2} x^{4}}{v})$

Step 16

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

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Step 16.1

Factor $v$ out of $- 9 v^{2} x^{4}$ .

$- (6 - \frac{8 x^{4}}{v} + \frac{v (- 9 v x^{4})}{v})$

Step 16.2

Cancel the common factors.

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Step 16.2.1

Raise $v$ to the power of $1$ .

$- (6 - \frac{8 x^{4}}{v} + \frac{v (- 9 v x^{4})}{v^{1}})$

Step 16.2.2

Factor $v$ out of $v^{1}$ .

$- (6 - \frac{8 x^{4}}{v} + \frac{v (- 9 v x^{4})}{v \cdot 1})$

Step 16.2.3

Cancel the common factor.

$- (6 - \frac{8 x^{4}}{v} + \frac{v (- 9 v x^{4})}{v \cdot 1})$

Step 16.2.4

Rewrite the expression.

$- (6 - \frac{8 x^{4}}{v} + \frac{- 9 v x^{4}}{1})$

Step 16.2.5

Divide $- 9 v x^{4}$ by $1$ .

$- (6 - \frac{8 x^{4}}{v} - 9 v x^{4})$