Pre-Algebra Examples

$(- 7 v^{3} x^{2} + 8 v^{2} x) \div (- 2 v^{3} x^{2})$

Step 1

Rewrite the division as a fraction.

$\frac{- 7 v^{3} x^{2} + 8 v^{2} x}{- 2 v^{3} x^{2}}$

Step 2

Factor $v^{2} x$ out of $- 7 v^{3} x^{2} + 8 v^{2} x$ .

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Step 2.1

Factor $v^{2} x$ out of $- 7 v^{3} x^{2}$ .

$\frac{v^{2} x (- 7 v x) + 8 v^{2} x}{- 2 v^{3} x^{2}}$

Step 2.2

Factor $v^{2} x$ out of $8 v^{2} x$ .

$\frac{v^{2} x (- 7 v x) + v^{2} x (8)}{- 2 v^{3} x^{2}}$

Step 2.3

Factor $v^{2} x$ out of $v^{2} x (- 7 v x) + v^{2} x (8)$ .

$\frac{v^{2} x (- 7 v x + 8)}{- 2 v^{3} x^{2}}$

Step 3

Cancel the common factor of $v^{2}$ and $v^{3}$ .

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Step 3.1

Factor $v^{2}$ out of $v^{2} x (- 7 v x + 8)$ .

$\frac{v^{2} (x (- 7 v x + 8))}{- 2 v^{3} x^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{v^{2} (x (- 7 v x + 8))}{v^{2} (- 2 v x^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{v^{2} (x (- 7 v x + 8))}{v^{2} (- 2 v x^{2})}$

Step 3.2.3

Rewrite the expression.

$\frac{x (- 7 v x + 8)}{- 2 v x^{2}}$

Step 4

Cancel the common factors.

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Step 4.1

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

$\frac{x (- 7 v x + 8)}{x (- 2 v x)}$

Step 4.2

Cancel the common factor.

$\frac{x (- 7 v x + 8)}{x (- 2 v x)}$

Step 4.3

Rewrite the expression.

$\frac{- 7 v x + 8}{- 2 v x}$

Step 5

Move the negative in front of the fraction.

$- \frac{- 7 v x + 8}{2 v x}$

Step 6

Factor $- 1$ out of $- 7 v x$ .

$- \frac{- (7 v x) + 8}{2 v x}$

Step 7

Rewrite $8$ as $- 1 (- 8)$ .

$- \frac{- (7 v x) - 1 (- 8)}{2 v x}$

Step 8

Factor $- 1$ out of $- (7 v x) - 1 (- 8)$ .

$- \frac{- (7 v x - 8)}{2 v x}$

Step 9

Rewrite $- (7 v x - 8)$ as $- 1 (7 v x - 8)$ .

$- \frac{- 1 (7 v x - 8)}{2 v x}$

Step 10

Move the negative in front of the fraction.

$- - \frac{7 v x - 8}{2 v x}$

Step 11

Multiply $- 1$ by $- 1$ .

$1 \frac{7 v x - 8}{2 v x}$

Step 12

Multiply $\frac{7 v x - 8}{2 v x}$ by $1$ .

$\frac{7 v x - 8}{2 v x}$

Step 13

Split the fraction $\frac{7 v x - 8}{2 v x}$ into two fractions.

$\frac{7 v x}{2 v x} + \frac{- 8}{2 v x}$

Step 14

Cancel the common factor of $v$ .

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Step 14.1

Cancel the common factor.

$\frac{7 v x}{2 v x} + \frac{- 8}{2 v x}$

Step 14.2

Rewrite the expression.

$\frac{7 x}{2 x} + \frac{- 8}{2 v x}$

Step 15

Cancel the common factor of $x$ .

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Step 15.1

Cancel the common factor.

$\frac{7 x}{2 x} + \frac{- 8}{2 v x}$

Step 15.2

Rewrite the expression.

$\frac{7}{2} + \frac{- 8}{2 v x}$

Step 16

Cancel the common factor of $- 8$ and $2$ .

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Step 16.1

Factor $2$ out of $- 8$ .

$\frac{7}{2} + \frac{2 \cdot - 4}{2 v x}$

Step 16.2

Cancel the common factors.

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Step 16.2.1

Factor $2$ out of $2 v x$ .

$\frac{7}{2} + \frac{2 \cdot - 4}{2 (v x)}$

Step 16.2.2

Cancel the common factor.

$\frac{7}{2} + \frac{2 \cdot - 4}{2 (v x)}$

Step 16.2.3

Rewrite the expression.

$\frac{7}{2} + \frac{- 4}{v x}$

Step 17

Move the negative in front of the fraction.

$\frac{7}{2} - \frac{4}{v x}$