Algebra Examples

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

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

Step 1

Factor

3 x

$3 x$ out of

- 24 x^{7} + 9 x^{3} - 15 x

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

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Step 1.1

Factor

3 x

$3 x$ out of

- 24 x^{7}

$- 24 x^{7}$ .

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

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

Step 1.2

Factor

3 x

$3 x$ out of

9 x^{3}

$9 x^{3}$ .

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

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

Step 1.3

Factor

3 x

$3 x$ out of

- 15 x

$- 15 x$ .

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

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

Step 1.4

Factor

3 x

$3 x$ out of

3 x (- 8 x^{6}) + 3 x (3 x^{2})

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

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

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

Step 1.5

Factor

3 x

$3 x$ out of

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

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

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

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

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

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

Step 2

Cancel the common factor of

3

$3$ .

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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.

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