Algebra Examples

$\frac{- 24 x^{7} + 9 x^{3} - 15 x}{3 x^{5}}$

Step 1

Factor $3 x$ out of $- 24 x^{7} + 9 x^{3} - 15 x$ .

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Step 1.1

Factor $3 x$ out of $- 24 x^{7}$ .

$\frac{3 x (- 8 x^{6}) + 9 x^{3} - 15 x}{3 x^{5}}$

Step 1.2

Factor $3 x$ out of $9 x^{3}$ .

$\frac{3 x (- 8 x^{6}) + 3 x (3 x^{2}) - 15 x}{3 x^{5}}$

Step 1.3

Factor $3 x$ out of $- 15 x$ .

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

Step 1.4

Factor $3 x$ out of $3 x (- 8 x^{6}) + 3 x (3 x^{2})$ .

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

Step 1.5

Factor $3 x$ out of $3 x (- 8 x^{6} + 3 x^{2}) + 3 x (- 5)$ .

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

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Cancel the common factors.

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Step 3.1

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

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

Factor $- 1$ out of $- 8 x^{6}$ .

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

Step 5

Factor $- 1$ out of $3 x^{2}$ .

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

Step 6

Factor $- 1$ out of $- (8 x^{6}) - (- 3 x^{2})$ .

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

Step 7

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- (8 x^{6} - 3 x^{2}) - 1 (5)}{x^{4}}$

Step 8

Factor $- 1$ out of $- (8 x^{6} - 3 x^{2}) - 1 (5)$ .

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

Step 9

Rewrite $- (8 x^{6} - 3 x^{2} + 5)$ as $- 1 (8 x^{6} - 3 x^{2} + 5)$ .

$\frac{- 1 (8 x^{6} - 3 x^{2} + 5)}{x^{4}}$

Step 10

Move the negative in front of the fraction.

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

Step 11

Split the fraction $\frac{8 x^{6} - 3 x^{2} + 5}{x^{4}}$ into two fractions.

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

Step 12

Split the fraction $\frac{8 x^{6} - 3 x^{2}}{x^{4}}$ into two fractions.

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

Step 13

Cancel the common factor of $x^{6}$ and $x^{4}$ .

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Step 13.1

Factor $x^{4}$ out of $8 x^{6}$ .

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

Step 13.2

Cancel the common factors.

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Step 13.2.1

Multiply by $1$ .

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

Step 13.2.2

Cancel the common factor.

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

Step 13.2.3

Rewrite the expression.

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

Step 13.2.4

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

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

Step 14

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

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Step 14.1

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

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

Step 14.2

Cancel the common factors.

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Step 14.2.1

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

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

Step 14.2.2

Cancel the common factor.

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

Step 14.2.3

Rewrite the expression.

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

Step 15

Move the negative in front of the fraction.

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