Pre-Algebra Examples

$(26 x^{4} v^{2} - 18 x^{2} v) \div (- 3 x^{4} v^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{26 x^{4} v^{2} - 18 x^{2} v}{- 3 x^{4} v^{2}}$

Step 2

Factor $2 x^{2} v$ out of $26 x^{4} v^{2} - 18 x^{2} v$ .

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Step 2.1

Factor $2 x^{2} v$ out of $26 x^{4} v^{2}$ .

$\frac{2 x^{2} v (13 x^{2} v) - 18 x^{2} v}{- 3 x^{4} v^{2}}$

Step 2.2

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

$\frac{2 x^{2} v (13 x^{2} v) + 2 x^{2} v (- 9)}{- 3 x^{4} v^{2}}$

Step 2.3

Factor $2 x^{2} v$ out of $2 x^{2} v (13 x^{2} v) + 2 x^{2} v (- 9)$ .

$\frac{2 x^{2} v (13 x^{2} v - 9)}{- 3 x^{4} v^{2}}$

Step 3

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

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Step 3.1

Factor $x^{2}$ out of $2 x^{2} v (13 x^{2} v - 9)$ .

$\frac{x^{2} (2 v (13 x^{2} v - 9))}{- 3 x^{4} v^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{2}$ out of $- 3 x^{4} v^{2}$ .

$\frac{x^{2} (2 v (13 x^{2} v - 9))}{x^{2} (- 3 x^{2} v^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{2} (2 v (13 x^{2} v - 9))}{x^{2} (- 3 x^{2} v^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{2 v (13 x^{2} v - 9)}{- 3 x^{2} v^{2}}$

Step 4

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

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Step 4.1

Factor $v$ out of $2 v (13 x^{2} v - 9)$ .

$\frac{v (2 (13 x^{2} v - 9))}{- 3 x^{2} v^{2}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $v$ out of $- 3 x^{2} v^{2}$ .

$\frac{v (2 (13 x^{2} v - 9))}{v (- 3 x^{2} v)}$

Step 4.2.2

Cancel the common factor.

$\frac{v (2 (13 x^{2} v - 9))}{v (- 3 x^{2} v)}$

Step 4.2.3

Rewrite the expression.

$\frac{2 (13 x^{2} v - 9)}{- 3 x^{2} v}$

Step 5

Move the negative in front of the fraction.

$- \frac{2 (13 x^{2} v - 9)}{3 x^{2} v}$

Step 6

Apply the distributive property.

$- \frac{2 (13 x^{2} v) + 2 \cdot - 9}{3 x^{2} v}$

Step 7

Multiply $13$ by $2$ .

$- \frac{26 (x^{2} v) + 2 \cdot - 9}{3 x^{2} v}$

Step 8

Multiply $2$ by $- 9$ .

$- \frac{26 x^{2} v - 18}{3 x^{2} v}$

Step 9

Split the fraction $\frac{26 x^{2} v - 18}{3 x^{2} v}$ into two fractions.

$- (\frac{26 x^{2} v}{3 x^{2} v} + \frac{- 18}{3 x^{2} v})$

Step 10

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

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Step 10.1

Cancel the common factor.

$- (\frac{26 x^{2} v}{3 x^{2} v} + \frac{- 18}{3 x^{2} v})$

Step 10.2

Rewrite the expression.

$- (\frac{26 v}{3 v} + \frac{- 18}{3 x^{2} v})$

Step 11

Cancel the common factor of $v$ .

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Step 11.1

Cancel the common factor.

$- (\frac{26 v}{3 v} + \frac{- 18}{3 x^{2} v})$

Step 11.2

Rewrite the expression.

$- (\frac{26}{3} + \frac{- 18}{3 x^{2} v})$

Step 12

Cancel the common factor of $- 18$ and $3$ .

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Step 12.1

Factor $3$ out of $- 18$ .

$- (\frac{26}{3} + \frac{3 \cdot - 6}{3 x^{2} v})$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Factor $3$ out of $3 x^{2} v$ .

$- (\frac{26}{3} + \frac{3 \cdot - 6}{3 (x^{2} v)})$

Step 12.2.2

Cancel the common factor.

$- (\frac{26}{3} + \frac{3 \cdot - 6}{3 (x^{2} v)})$

Step 12.2.3

Rewrite the expression.

$- (\frac{26}{3} + \frac{- 6}{x^{2} v})$

Step 13

Move the negative in front of the fraction.

$- (\frac{26}{3} - \frac{6}{x^{2} v})$