Pre-Algebra Examples

$(- 6 x^{3} v + 17 x^{4} v^{2}) \div (- 3 x^{4} v^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{- 6 x^{3} v + 17 x^{4} v^{2}}{- 3 x^{4} v^{2}}$

Step 2

Factor $x^{3} v$ out of $- 6 x^{3} v + 17 x^{4} v^{2}$ .

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Step 2.1

Factor $x^{3} v$ out of $- 6 x^{3} v$ .

$\frac{x^{3} v (- 6) + 17 x^{4} v^{2}}{- 3 x^{4} v^{2}}$

Step 2.2

Factor $x^{3} v$ out of $17 x^{4} v^{2}$ .

$\frac{x^{3} v (- 6) + x^{3} v (17 x v)}{- 3 x^{4} v^{2}}$

Step 2.3

Factor $x^{3} v$ out of $x^{3} v (- 6) + x^{3} v (17 x v)$ .

$\frac{x^{3} v (- 6 + 17 x v)}{- 3 x^{4} v^{2}}$

Step 3

Cancel the common factor of $x^{3}$ and $x^{4}$ .

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Step 3.1

Factor $x^{3}$ out of $x^{3} v (- 6 + 17 x v)$ .

$\frac{x^{3} (v (- 6 + 17 x v))}{- 3 x^{4} v^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{x^{3} (v (- 6 + 17 x v))}{x^{3} (- 3 x v^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{3} (v (- 6 + 17 x v))}{x^{3} (- 3 x v^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{v (- 6 + 17 x v)}{- 3 x v^{2}}$

Step 4

Cancel the common factors.

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Step 4.1

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

$\frac{v (- 6 + 17 x v)}{v (- 3 x v)}$

Step 4.2

Cancel the common factor.

$\frac{v (- 6 + 17 x v)}{v (- 3 x v)}$

Step 4.3

Rewrite the expression.

$\frac{- 6 + 17 x v}{- 3 x v}$

Step 5

Move the negative in front of the fraction.

$- \frac{- 6 + 17 x v}{3 x v}$

Step 6

Rewrite $- 6$ as $- 1 (6)$ .

$- \frac{- 1 (6) + 17 x v}{3 x v}$

Step 7

Factor $- 1$ out of $17 x v$ .

$- \frac{- 1 (6) - (- 17 x v)}{3 x v}$

Step 8

Factor $- 1$ out of $- 1 (6) - (- 17 x v)$ .

$- \frac{- 1 (6 - 17 x v)}{3 x v}$

Step 9

Move the negative in front of the fraction.

$- - \frac{6 - 17 x v}{3 x v}$

Step 10

Multiply $- 1$ by $- 1$ .

$1 \frac{6 - 17 x v}{3 x v}$

Step 11

Multiply $\frac{6 - 17 x v}{3 x v}$ by $1$ .

$\frac{6 - 17 x v}{3 x v}$

Step 12

Split the fraction $\frac{6 - 17 x v}{3 x v}$ into two fractions.

$\frac{6}{3 x v} + \frac{- 17 x v}{3 x v}$

Step 13

Cancel the common factor of $6$ and $3$ .

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Step 13.1

Factor $3$ out of $6$ .

$\frac{3 \cdot 2}{3 x v} + \frac{- 17 x v}{3 x v}$

Step 13.2

Cancel the common factors.

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Step 13.2.1

Factor $3$ out of $3 x v$ .

$\frac{3 \cdot 2}{3 (x v)} + \frac{- 17 x v}{3 x v}$

Step 13.2.2

Cancel the common factor.

$\frac{3 \cdot 2}{3 (x v)} + \frac{- 17 x v}{3 x v}$

Step 13.2.3

Rewrite the expression.

$\frac{2}{x v} + \frac{- 17 x v}{3 x v}$

Step 14

Cancel the common factor of $x$ .

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Step 14.1

Cancel the common factor.

$\frac{2}{x v} + \frac{- 17 x v}{3 x v}$

Step 14.2

Rewrite the expression.

$\frac{2}{x v} + \frac{- 17 v}{3 v}$

Step 15

Cancel the common factor of $v$ .

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Step 15.1

Cancel the common factor.

$\frac{2}{x v} + \frac{- 17 v}{3 v}$

Step 15.2

Rewrite the expression.

$\frac{2}{x v} + \frac{- 17}{3}$

Step 16

Move the negative in front of the fraction.

$\frac{2}{x v} - \frac{17}{3}$