Pre-Algebra Examples

$\frac{32 z^{5} x^{5} - 9 z^{5} x^{3}}{- 4 z^{3} x^{4}}$

Step 1

Factor $z^{5} x^{3}$ out of $32 z^{5} x^{5} - 9 z^{5} x^{3}$ .

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Step 1.1

Factor $z^{5} x^{3}$ out of $32 z^{5} x^{5}$ .

$\frac{z^{5} x^{3} (32 x^{2}) - 9 z^{5} x^{3}}{- 4 z^{3} x^{4}}$

Step 1.2

Factor $z^{5} x^{3}$ out of $- 9 z^{5} x^{3}$ .

$\frac{z^{5} x^{3} (32 x^{2}) + z^{5} x^{3} (- 9)}{- 4 z^{3} x^{4}}$

Step 1.3

Factor $z^{5} x^{3}$ out of $z^{5} x^{3} (32 x^{2}) + z^{5} x^{3} (- 9)$ .

$\frac{z^{5} x^{3} (32 x^{2} - 9)}{- 4 z^{3} x^{4}}$

Step 2

Cancel the common factor of $z^{5}$ and $z^{3}$ .

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Step 2.1

Factor $z^{3}$ out of $z^{5} x^{3} (32 x^{2} - 9)$ .

$\frac{z^{3} (z^{2} x^{3} (32 x^{2} - 9))}{- 4 z^{3} x^{4}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\frac{z^{3} (z^{2} x^{3} (32 x^{2} - 9))}{z^{3} (- 4 x^{4})}$

Step 2.2.2

Cancel the common factor.

$\frac{z^{3} (z^{2} x^{3} (32 x^{2} - 9))}{z^{3} (- 4 x^{4})}$

Step 2.2.3

Rewrite the expression.

$\frac{z^{2} x^{3} (32 x^{2} - 9)}{- 4 x^{4}}$

Step 3

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

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Step 3.1

Factor $x^{3}$ out of $z^{2} x^{3} (32 x^{2} - 9)$ .

$\frac{x^{3} (z^{2} (32 x^{2} - 9))}{- 4 x^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{x^{3} (z^{2} (32 x^{2} - 9))}{x^{3} (- 4 x)}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{3} (z^{2} (32 x^{2} - 9))}{x^{3} (- 4 x)}$

Step 3.2.3

Rewrite the expression.

$\frac{z^{2} (32 x^{2} - 9)}{- 4 x}$

Step 4

Move the negative in front of the fraction.

$- \frac{z^{2} (32 x^{2} - 9)}{4 x}$

Step 5

Apply the distributive property.

$- \frac{z^{2} (32 x^{2}) + z^{2} \cdot - 9}{4 x}$

Step 6

Rewrite using the commutative property of multiplication.

$- \frac{32 z^{2} x^{2} + z^{2} \cdot - 9}{4 x}$

Step 7

Move $- 9$ to the left of $z^{2}$ .

$- \frac{32 z^{2} x^{2} - 9 z^{2}}{4 x}$

Step 8

Split the fraction $\frac{32 z^{2} x^{2} - 9 z^{2}}{4 x}$ into two fractions.

$- (\frac{32 z^{2} x^{2}}{4 x} + \frac{- 9 z^{2}}{4 x})$

Step 9

Cancel the common factor of $32$ and $4$ .

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Step 9.1

Factor $4$ out of $32 z^{2} x^{2}$ .

$- (\frac{4 (8 z^{2} x^{2})}{4 x} + \frac{- 9 z^{2}}{4 x})$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $4$ out of $4 x$ .

$- (\frac{4 (8 z^{2} x^{2})}{4 (x)} + \frac{- 9 z^{2}}{4 x})$

Step 9.2.2

Cancel the common factor.

$- (\frac{4 (8 z^{2} x^{2})}{4 x} + \frac{- 9 z^{2}}{4 x})$

Step 9.2.3

Rewrite the expression.

$- (\frac{8 z^{2} x^{2}}{x} + \frac{- 9 z^{2}}{4 x})$

Step 10

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

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Step 10.1

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

$- (\frac{x (8 z^{2} x)}{x} + \frac{- 9 z^{2}}{4 x})$

Step 10.2

Cancel the common factors.

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Step 10.2.1

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

$- (\frac{x (8 z^{2} x)}{x^{1}} + \frac{- 9 z^{2}}{4 x})$

Step 10.2.2

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

$- (\frac{x (8 z^{2} x)}{x \cdot 1} + \frac{- 9 z^{2}}{4 x})$

Step 10.2.3

Cancel the common factor.

$- (\frac{x (8 z^{2} x)}{x \cdot 1} + \frac{- 9 z^{2}}{4 x})$

Step 10.2.4

Rewrite the expression.

$- (\frac{8 z^{2} x}{1} + \frac{- 9 z^{2}}{4 x})$

Step 10.2.5

Divide $8 z^{2} x$ by $1$ .

$- (8 z^{2} x + \frac{- 9 z^{2}}{4 x})$

Step 11

Move the negative in front of the fraction.

$- (8 z^{2} x - \frac{9 z^{2}}{4 x})$