Pre-Algebra Examples

$\frac{- 15 x^{8} + 6 x^{4} - 9}{3 x^{2}}$

Step 1

Cancel the common factor of $- 15 x^{8} + 6 x^{4} - 9$ and $3$ .

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Step 1.1

Factor $3$ out of $- 15 x^{8}$ .

$\frac{3 (- 5 x^{8}) + 6 x^{4} - 9}{3 x^{2}}$

Step 1.2

Factor $3$ out of $6 x^{4}$ .

$\frac{3 (- 5 x^{8}) + 3 (2 x^{4}) - 9}{3 x^{2}}$

Step 1.3

Factor $3$ out of $3 (- 5 x^{8}) + 3 (2 x^{4})$ .

$\frac{3 (- 5 x^{8} + 2 x^{4}) - 9}{3 x^{2}}$

Step 1.4

Factor $3$ out of $- 9$ .

$\frac{3 (- 5 x^{8} + 2 x^{4}) + 3 \cdot - 3}{3 x^{2}}$

Step 1.5

Factor $3$ out of $3 (- 5 x^{8} + 2 x^{4}) + 3 (- 3)$ .

$\frac{3 (- 5 x^{8} + 2 x^{4} - 3)}{3 x^{2}}$

Step 1.6

Cancel the common factors.

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Step 1.6.1

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

$\frac{3 (- 5 x^{8} + 2 x^{4} - 3)}{3 (x^{2})}$

Step 1.6.2

Cancel the common factor.

$\frac{3 (- 5 x^{8} + 2 x^{4} - 3)}{3 x^{2}}$

Step 1.6.3

Rewrite the expression.

$\frac{- 5 x^{8} + 2 x^{4} - 3}{x^{2}}$

Step 2

Factor $- 1$ out of $- 5 x^{8}$ .

$\frac{- (5 x^{8}) + 2 x^{4} - 3}{x^{2}}$

Step 3

Factor $- 1$ out of $2 x^{4}$ .

$\frac{- (5 x^{8}) - (- 2 x^{4}) - 3}{x^{2}}$

Step 4

Factor $- 1$ out of $- (5 x^{8}) - (- 2 x^{4})$ .

$\frac{- (5 x^{8} - 2 x^{4}) - 3}{x^{2}}$

Step 5

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- (5 x^{8} - 2 x^{4}) - 1 (3)}{x^{2}}$

Step 6

Factor $- 1$ out of $- (5 x^{8} - 2 x^{4}) - 1 (3)$ .

$\frac{- (5 x^{8} - 2 x^{4} + 3)}{x^{2}}$

Step 7

Rewrite $- (5 x^{8} - 2 x^{4} + 3)$ as $- 1 (5 x^{8} - 2 x^{4} + 3)$ .

$\frac{- 1 (5 x^{8} - 2 x^{4} + 3)}{x^{2}}$

Step 8

Move the negative in front of the fraction.

$- \frac{5 x^{8} - 2 x^{4} + 3}{x^{2}}$

Step 9

Split the fraction $\frac{5 x^{8} - 2 x^{4} + 3}{x^{2}}$ into two fractions.

$- (\frac{5 x^{8} - 2 x^{4}}{x^{2}} + \frac{3}{x^{2}})$

Step 10

Split the fraction $\frac{5 x^{8} - 2 x^{4}}{x^{2}}$ into two fractions.

$- (\frac{5 x^{8}}{x^{2}} + \frac{- 2 x^{4}}{x^{2}} + \frac{3}{x^{2}})$

Step 11

Cancel the common factor of $x^{8}$ and $x^{2}$ .

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Step 11.1

Factor $x^{2}$ out of $5 x^{8}$ .

$- (\frac{x^{2} (5 x^{6})}{x^{2}} + \frac{- 2 x^{4}}{x^{2}} + \frac{3}{x^{2}})$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Multiply by $1$ .

$- (\frac{x^{2} (5 x^{6})}{x^{2} \cdot 1} + \frac{- 2 x^{4}}{x^{2}} + \frac{3}{x^{2}})$

Step 11.2.2

Cancel the common factor.

$- (\frac{x^{2} (5 x^{6})}{x^{2} \cdot 1} + \frac{- 2 x^{4}}{x^{2}} + \frac{3}{x^{2}})$

Step 11.2.3

Rewrite the expression.

$- (\frac{5 x^{6}}{1} + \frac{- 2 x^{4}}{x^{2}} + \frac{3}{x^{2}})$

Step 11.2.4

Divide $5 x^{6}$ by $1$ .

$- (5 x^{6} + \frac{- 2 x^{4}}{x^{2}} + \frac{3}{x^{2}})$

Step 12

Cancel the common factor of $x^{4}$ and $x^{2}$ .

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Step 12.1

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

$- (5 x^{6} + \frac{x^{2} (- 2 x^{2})}{x^{2}} + \frac{3}{x^{2}})$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Multiply by $1$ .

$- (5 x^{6} + \frac{x^{2} (- 2 x^{2})}{x^{2} \cdot 1} + \frac{3}{x^{2}})$

Step 12.2.2

Cancel the common factor.

$- (5 x^{6} + \frac{x^{2} (- 2 x^{2})}{x^{2} \cdot 1} + \frac{3}{x^{2}})$

Step 12.2.3

Rewrite the expression.

$- (5 x^{6} + \frac{- 2 x^{2}}{1} + \frac{3}{x^{2}})$

Step 12.2.4

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

$- (5 x^{6} - 2 x^{2} + \frac{3}{x^{2}})$