Pre-Algebra Examples

$\frac{- 10 x^{8} + 8 x^{7} - 4}{2 x^{2}}$

Step 1

Cancel the common factor of $- 10 x^{8} + 8 x^{7} - 4$ and $2$ .

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Step 1.1

Factor $2$ out of $- 10 x^{8}$ .

$\frac{2 (- 5 x^{8}) + 8 x^{7} - 4}{2 x^{2}}$

Step 1.2

Factor $2$ out of $8 x^{7}$ .

$\frac{2 (- 5 x^{8}) + 2 (4 x^{7}) - 4}{2 x^{2}}$

Step 1.3

Factor $2$ out of $2 (- 5 x^{8}) + 2 (4 x^{7})$ .

$\frac{2 (- 5 x^{8} + 4 x^{7}) - 4}{2 x^{2}}$

Step 1.4

Factor $2$ out of $- 4$ .

$\frac{2 (- 5 x^{8} + 4 x^{7}) + 2 \cdot - 2}{2 x^{2}}$

Step 1.5

Factor $2$ out of $2 (- 5 x^{8} + 4 x^{7}) + 2 (- 2)$ .

$\frac{2 (- 5 x^{8} + 4 x^{7} - 2)}{2 x^{2}}$

Step 1.6

Cancel the common factors.

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Step 1.6.1

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

$\frac{2 (- 5 x^{8} + 4 x^{7} - 2)}{2 (x^{2})}$

Step 1.6.2

Cancel the common factor.

$\frac{2 (- 5 x^{8} + 4 x^{7} - 2)}{2 x^{2}}$

Step 1.6.3

Rewrite the expression.

$\frac{- 5 x^{8} + 4 x^{7} - 2}{x^{2}}$

Step 2

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

$\frac{- (5 x^{8}) + 4 x^{7} - 2}{x^{2}}$

Step 3

Factor $- 1$ out of $4 x^{7}$ .

$\frac{- (5 x^{8}) - (- 4 x^{7}) - 2}{x^{2}}$

Step 4

Factor $- 1$ out of $- (5 x^{8}) - (- 4 x^{7})$ .

$\frac{- (5 x^{8} - 4 x^{7}) - 2}{x^{2}}$

Step 5

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{- (5 x^{8} - 4 x^{7}) - 1 (2)}{x^{2}}$

Step 6

Factor $- 1$ out of $- (5 x^{8} - 4 x^{7}) - 1 (2)$ .

$\frac{- (5 x^{8} - 4 x^{7} + 2)}{x^{2}}$

Step 7

Rewrite $- (5 x^{8} - 4 x^{7} + 2)$ as $- 1 (5 x^{8} - 4 x^{7} + 2)$ .

$\frac{- 1 (5 x^{8} - 4 x^{7} + 2)}{x^{2}}$

Step 8

Move the negative in front of the fraction.

$- \frac{5 x^{8} - 4 x^{7} + 2}{x^{2}}$

Step 9

Split the fraction $\frac{5 x^{8} - 4 x^{7} + 2}{x^{2}}$ into two fractions.

$- (\frac{5 x^{8} - 4 x^{7}}{x^{2}} + \frac{2}{x^{2}})$

Step 10

Split the fraction $\frac{5 x^{8} - 4 x^{7}}{x^{2}}$ into two fractions.

$- (\frac{5 x^{8}}{x^{2}} + \frac{- 4 x^{7}}{x^{2}} + \frac{2}{x^{2}})$

Step 11

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

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Step 11.1

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

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

Step 11.2

Cancel the common factors.

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Step 11.2.1

Multiply by $1$ .

$- (\frac{x^{2} (5 x^{6})}{x^{2} \cdot 1} + \frac{- 4 x^{7}}{x^{2}} + \frac{2}{x^{2}})$

Step 11.2.2

Cancel the common factor.

$- (\frac{x^{2} (5 x^{6})}{x^{2} \cdot 1} + \frac{- 4 x^{7}}{x^{2}} + \frac{2}{x^{2}})$

Step 11.2.3

Rewrite the expression.

$- (\frac{5 x^{6}}{1} + \frac{- 4 x^{7}}{x^{2}} + \frac{2}{x^{2}})$

Step 11.2.4

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

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

Step 12

Cancel the common factor of $x^{7}$ and $x^{2}$ .

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Step 12.1

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

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

Step 12.2

Cancel the common factors.

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Step 12.2.1

Multiply by $1$ .

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

Step 12.2.2

Cancel the common factor.

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

Step 12.2.3

Rewrite the expression.

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

Step 12.2.4

Divide $- 4 x^{5}$ by $1$ .

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