Pre-Algebra Examples

$(- 12 z^{4} x^{2} - 14 z^{5} x + 4 z^{5} x^{7}) \div 2 z^{4} x^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{- 12 z^{4} x^{2} - 14 z^{5} x + 4 z^{5} x^{7}}{2 z^{4} x^{2}}$

Step 2

Factor $2 z^{4} x$ out of $- 12 z^{4} x^{2} - 14 z^{5} x + 4 z^{5} x^{7}$ .

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Step 2.1

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

$\frac{2 z^{4} x (- 6 x) - 14 z^{5} x + 4 z^{5} x^{7}}{2 z^{4} x^{2}}$

Step 2.2

Factor $2 z^{4} x$ out of $- 14 z^{5} x$ .

$\frac{2 z^{4} x (- 6 x) + 2 z^{4} x (- 7 z) + 4 z^{5} x^{7}}{2 z^{4} x^{2}}$

Step 2.3

Factor $2 z^{4} x$ out of $4 z^{5} x^{7}$ .

$\frac{2 z^{4} x (- 6 x) + 2 z^{4} x (- 7 z) + 2 z^{4} x (2 z x^{6})}{2 z^{4} x^{2}}$

Step 2.4

Factor $2 z^{4} x$ out of $2 z^{4} x (- 6 x) + 2 z^{4} x (- 7 z)$ .

$\frac{2 z^{4} x (- 6 x - 7 z) + 2 z^{4} x (2 z x^{6})}{2 z^{4} x^{2}}$

Step 2.5

Factor $2 z^{4} x$ out of $2 z^{4} x (- 6 x - 7 z) + 2 z^{4} x (2 z x^{6})$ .

$\frac{2 z^{4} x (- 6 x - 7 z + 2 z x^{6})}{2 z^{4} x^{2}}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$\frac{2 z^{4} x (- 6 x - 7 z + 2 z x^{6})}{2 z^{4} x^{2}}$

Step 3.2

Rewrite the expression.

$\frac{z^{4} x (- 6 x - 7 z + 2 z x^{6})}{z^{4} x^{2}}$

Step 4

Cancel the common factor of $z^{4}$ .

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Step 4.1

Cancel the common factor.

$\frac{z^{4} x (- 6 x - 7 z + 2 z x^{6})}{z^{4} x^{2}}$

Step 4.2

Rewrite the expression.

$\frac{x (- 6 x - 7 z + 2 z x^{6})}{x^{2}}$

Step 5

Cancel the common factors.

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Step 5.1

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

$\frac{x (- 6 x - 7 z + 2 z x^{6})}{x \cdot x}$

Step 5.2

Cancel the common factor.

$\frac{x (- 6 x - 7 z + 2 z x^{6})}{x \cdot x}$

Step 5.3

Rewrite the expression.

$\frac{- 6 x - 7 z + 2 z x^{6}}{x}$

Step 6

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

$\frac{- (6 x) - 7 z + 2 z x^{6}}{x}$

Step 7

Factor $- 1$ out of $- 7 z$ .

$\frac{- (6 x) - (7 z) + 2 z x^{6}}{x}$

Step 8

Factor $- 1$ out of $- (6 x) - (7 z)$ .

$\frac{- (6 x + 7 z) + 2 z x^{6}}{x}$

Step 9

Factor $- 1$ out of $2 z x^{6}$ .

$\frac{- (6 x + 7 z) - (- 2 z x^{6})}{x}$

Step 10

Factor $- 1$ out of $- (6 x + 7 z) - (- 2 z x^{6})$ .

$\frac{- (6 x + 7 z - 2 z x^{6})}{x}$

Step 11

Rewrite $- (6 x + 7 z - 2 z x^{6})$ as $- 1 (6 x + 7 z - 2 z x^{6})$ .

$\frac{- 1 (6 x + 7 z - 2 z x^{6})}{x}$

Step 12

Move the negative in front of the fraction.

$- \frac{6 x + 7 z - 2 z x^{6}}{x}$

Step 13

Split the fraction $\frac{6 x + 7 z - 2 z x^{6}}{x}$ into two fractions.

$- (\frac{6 x + 7 z}{x} + \frac{- 2 z x^{6}}{x})$

Step 14

Split the fraction $\frac{6 x + 7 z}{x}$ into two fractions.

$- (\frac{6 x}{x} + \frac{7 z}{x} + \frac{- 2 z x^{6}}{x})$

Step 15

Cancel the common factor of $x$ .

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Step 15.1

Cancel the common factor.

$- (\frac{6 x}{x} + \frac{7 z}{x} + \frac{- 2 z x^{6}}{x})$

Step 15.2

Divide $6$ by $1$ .

$- (6 + \frac{7 z}{x} + \frac{- 2 z x^{6}}{x})$

Step 16

Cancel the common factor of $x^{6}$ and $x$ .

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Step 16.1

Factor $x$ out of $- 2 z x^{6}$ .

$- (6 + \frac{7 z}{x} + \frac{x (- 2 z x^{5})}{x})$

Step 16.2

Cancel the common factors.

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Step 16.2.1

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

$- (6 + \frac{7 z}{x} + \frac{x (- 2 z x^{5})}{x^{1}})$

Step 16.2.2

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

$- (6 + \frac{7 z}{x} + \frac{x (- 2 z x^{5})}{x \cdot 1})$

Step 16.2.3

Cancel the common factor.

$- (6 + \frac{7 z}{x} + \frac{x (- 2 z x^{5})}{x \cdot 1})$

Step 16.2.4

Rewrite the expression.

$- (6 + \frac{7 z}{x} + \frac{- 2 z x^{5}}{1})$

Step 16.2.5

Divide $- 2 z x^{5}$ by $1$ .

$- (6 + \frac{7 z}{x} - 2 z x^{5})$