Pre-Algebra Examples

$(36 x^{3} z^{4} + 28 x^{6} z^{7} - 12 x z^{7}) \div 4 x^{3} z^{4}$

Step 1

Rewrite the division as a fraction.

$\frac{36 x^{3} z^{4} + 28 x^{6} z^{7} - 12 x z^{7}}{4 x^{3} z^{4}}$

Step 2

Factor $4 x z^{4}$ out of $36 x^{3} z^{4} + 28 x^{6} z^{7} - 12 x z^{7}$ .

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Step 2.1

Factor $4 x z^{4}$ out of $36 x^{3} z^{4}$ .

$\frac{4 x z^{4} (9 x^{2}) + 28 x^{6} z^{7} - 12 x z^{7}}{4 x^{3} z^{4}}$

Step 2.2

Factor $4 x z^{4}$ out of $28 x^{6} z^{7}$ .

$\frac{4 x z^{4} (9 x^{2}) + 4 x z^{4} (7 x^{5} z^{3}) - 12 x z^{7}}{4 x^{3} z^{4}}$

Step 2.3

Factor $4 x z^{4}$ out of $- 12 x z^{7}$ .

$\frac{4 x z^{4} (9 x^{2}) + 4 x z^{4} (7 x^{5} z^{3}) + 4 x z^{4} (- 3 z^{3})}{4 x^{3} z^{4}}$

Step 2.4

Factor $4 x z^{4}$ out of $4 x z^{4} (9 x^{2}) + 4 x z^{4} (7 x^{5} z^{3})$ .

$\frac{4 x z^{4} (9 x^{2} + 7 x^{5} z^{3}) + 4 x z^{4} (- 3 z^{3})}{4 x^{3} z^{4}}$

Step 2.5

Factor $4 x z^{4}$ out of $4 x z^{4} (9 x^{2} + 7 x^{5} z^{3}) + 4 x z^{4} (- 3 z^{3})$ .

$\frac{4 x z^{4} (9 x^{2} + 7 x^{5} z^{3} - 3 z^{3})}{4 x^{3} z^{4}}$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Cancel the common factor.

$\frac{4 x z^{4} (9 x^{2} + 7 x^{5} z^{3} - 3 z^{3})}{4 x^{3} z^{4}}$

Step 3.2

Rewrite the expression.

$\frac{x z^{4} (9 x^{2} + 7 x^{5} z^{3} - 3 z^{3})}{x^{3} z^{4}}$

Step 4

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

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Step 4.1

Factor $x$ out of $x z^{4} (9 x^{2} + 7 x^{5} z^{3} - 3 z^{3})$ .

$\frac{x (z^{4} (9 x^{2} + 7 x^{5} z^{3} - 3 z^{3}))}{x^{3} z^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x$ out of $x^{3} z^{4}$ .

$\frac{x (z^{4} (9 x^{2} + 7 x^{5} z^{3} - 3 z^{3}))}{x (x^{2} z^{4})}$

Step 4.2.2

Cancel the common factor.

$\frac{x (z^{4} (9 x^{2} + 7 x^{5} z^{3} - 3 z^{3}))}{x (x^{2} z^{4})}$

Step 4.2.3

Rewrite the expression.

$\frac{z^{4} (9 x^{2} + 7 x^{5} z^{3} - 3 z^{3})}{x^{2} z^{4}}$

Step 5

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

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Step 5.1

Cancel the common factor.

$\frac{z^{4} (9 x^{2} + 7 x^{5} z^{3} - 3 z^{3})}{x^{2} z^{4}}$

Step 5.2

Rewrite the expression.

$\frac{9 x^{2} + 7 x^{5} z^{3} - 3 z^{3}}{x^{2}}$

Step 6

Split the fraction $\frac{9 x^{2} + 7 x^{5} z^{3} - 3 z^{3}}{x^{2}}$ into two fractions.

$\frac{9 x^{2} + 7 x^{5} z^{3}}{x^{2}} + \frac{- 3 z^{3}}{x^{2}}$

Step 7

Split the fraction $\frac{9 x^{2} + 7 x^{5} z^{3}}{x^{2}}$ into two fractions.

$\frac{9 x^{2}}{x^{2}} + \frac{7 x^{5} z^{3}}{x^{2}} + \frac{- 3 z^{3}}{x^{2}}$

Step 8

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

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Step 8.1

Cancel the common factor.

$\frac{9 x^{2}}{x^{2}} + \frac{7 x^{5} z^{3}}{x^{2}} + \frac{- 3 z^{3}}{x^{2}}$

Step 8.2

Divide $9$ by $1$ .

$9 + \frac{7 x^{5} z^{3}}{x^{2}} + \frac{- 3 z^{3}}{x^{2}}$

Step 9

Cancel the common factor of $x^{5}$ and $x^{2}$ .

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Step 9.1

Factor $x^{2}$ out of $7 x^{5} z^{3}$ .

$9 + \frac{x^{2} (7 x^{3} z^{3})}{x^{2}} + \frac{- 3 z^{3}}{x^{2}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Multiply by $1$ .

$9 + \frac{x^{2} (7 x^{3} z^{3})}{x^{2} \cdot 1} + \frac{- 3 z^{3}}{x^{2}}$

Step 9.2.2

Cancel the common factor.

$9 + \frac{x^{2} (7 x^{3} z^{3})}{x^{2} \cdot 1} + \frac{- 3 z^{3}}{x^{2}}$

Step 9.2.3

Rewrite the expression.

$9 + \frac{7 x^{3} z^{3}}{1} + \frac{- 3 z^{3}}{x^{2}}$

Step 9.2.4

Divide $7 x^{3} z^{3}$ by $1$ .

$9 + 7 x^{3} z^{3} + \frac{- 3 z^{3}}{x^{2}}$

Step 10

Move the negative in front of the fraction.

$9 + 7 x^{3} z^{3} - \frac{3 z^{3}}{x^{2}}$