Algebra Examples

(- x^{6} + x^{5} + 7 x^{2} - 9) \div x^{4}

$(- x^{6} + x^{5} + 7 x^{2} - 9) \div x^{4}$

Step 1

Rewrite the division as a fraction.

\frac{- x^{6} + x^{5} + 7 x^{2} - 9}{x^{4}}

$\frac{- x^{6} + x^{5} + 7 x^{2} - 9}{x^{4}}$

Step 2

Factor

- 1

$- 1$ out of

- x^{6}

$- x^{6}$ .

\frac{- (x^{6}) + x^{5} + 7 x^{2} - 9}{x^{4}}

$\frac{- (x^{6}) + x^{5} + 7 x^{2} - 9}{x^{4}}$

Step 3

Factor

- 1

$- 1$ out of

x^{5}

$x^{5}$ .

\frac{- (x^{6}) - 1 (- x^{5}) + 7 x^{2} - 9}{x^{4}}

$\frac{- (x^{6}) - 1 (- x^{5}) + 7 x^{2} - 9}{x^{4}}$

Step 4

Factor

- 1

$- 1$ out of

- (x^{6}) - 1 (- x^{5})

$- (x^{6}) - 1 (- x^{5})$ .

\frac{- (x^{6} - x^{5}) + 7 x^{2} - 9}{x^{4}}

$\frac{- (x^{6} - x^{5}) + 7 x^{2} - 9}{x^{4}}$

Step 5

Factor

- 1

$- 1$ out of

7 x^{2}

$7 x^{2}$ .

\frac{- (x^{6} - x^{5}) - (- 7 x^{2}) - 9}{x^{4}}

$\frac{- (x^{6} - x^{5}) - (- 7 x^{2}) - 9}{x^{4}}$

Step 6

Factor

- 1

$- 1$ out of

- (x^{6} - x^{5}) - (- 7 x^{2})

$- (x^{6} - x^{5}) - (- 7 x^{2})$ .

\frac{- (x^{6} - x^{5} - 7 x^{2}) - 9}{x^{4}}

$\frac{- (x^{6} - x^{5} - 7 x^{2}) - 9}{x^{4}}$

Step 7

Rewrite

- 9

$- 9$ as

- 1 (9)

$- 1 (9)$ .

\frac{- (x^{6} - x^{5} - 7 x^{2}) - 1 (9)}{x^{4}}

$\frac{- (x^{6} - x^{5} - 7 x^{2}) - 1 (9)}{x^{4}}$

Step 8

Factor

$- 1$ out of

$- (x^{6} - x^{5} - 7 x^{2}) - 1 (9)$ .

$\frac{- (x^{6} - x^{5} - 7 x^{2} + 9)}{x^{4}}$

Step 9

Rewrite

$- (x^{6} - x^{5} - 7 x^{2} + 9)$ as

$- 1 (x^{6} - x^{5} - 7 x^{2} + 9)$ .

$\frac{- 1 (x^{6} - x^{5} - 7 x^{2} + 9)}{x^{4}}$

Step 10

Move the negative in front of the fraction.

$- \frac{x^{6} - x^{5} - 7 x^{2} + 9}{x^{4}}$

Step 11

Split the fraction

$\frac{x^{6} - x^{5} - 7 x^{2} + 9}{x^{4}}$ into two fractions.

$- (\frac{x^{6} - x^{5} - 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 12

Split the fraction

$\frac{x^{6} - x^{5} - 7 x^{2}}{x^{4}}$ into two fractions.

$- (\frac{x^{6} - x^{5}}{x^{4}} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 13

Split the fraction

$\frac{x^{6} - x^{5}}{x^{4}}$ into two fractions.

$- (\frac{x^{6}}{x^{4}} + \frac{- x^{5}}{x^{4}} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 14

Cancel the common factor of

$x^{6}$ and

$x^{4}$ .

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Step 14.1

Factor

$x^{4}$ out of

$x^{6}$ .

$- (\frac{x^{4} x^{2}}{x^{4}} + \frac{- x^{5}}{x^{4}} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 14.2

Cancel the common factors.

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Step 14.2.1

Multiply by

$1$ .

$- (\frac{x^{4} x^{2}}{x^{4} \cdot 1} + \frac{- x^{5}}{x^{4}} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 14.2.2

Cancel the common factor.

$- (\frac{x^{4} x^{2}}{x^{4} \cdot 1} + \frac{- x^{5}}{x^{4}} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 14.2.3

Rewrite the expression.

$- (\frac{x^{2}}{1} + \frac{- x^{5}}{x^{4}} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 14.2.4

Divide

$x^{2}$ by

$1$ .

$- (x^{2} + \frac{- x^{5}}{x^{4}} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 15

Cancel the common factor of

$x^{5}$ and

$x^{4}$ .

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Step 15.1

Factor

$x^{4}$ out of

$- x^{5}$ .

$- (x^{2} + \frac{x^{4} (- x)}{x^{4}} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 15.2

Cancel the common factors.

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Step 15.2.1

Multiply by

$1$ .

$- (x^{2} + \frac{x^{4} (- x)}{x^{4} \cdot 1} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 15.2.2

Cancel the common factor.

$- (x^{2} + \frac{x^{4} (- x)}{x^{4} \cdot 1} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 15.2.3

Rewrite the expression.

$- (x^{2} + \frac{- x}{1} + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 15.2.4

Divide

$- x$ by

$1$ .

$- (x^{2} - x + \frac{- 7 x^{2}}{x^{4}} + \frac{9}{x^{4}})$

Step 16

Cancel the common factor of

$x^{2}$ and

$x^{4}$ .

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Step 16.1

Factor

$x^{2}$ out of

$- 7 x^{2}$ .

$- (x^{2} - x + \frac{x^{2} \cdot - 7}{x^{4}} + \frac{9}{x^{4}})$

Step 16.2

Cancel the common factors.

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Step 16.2.1

Factor

$x^{2}$ out of

$x^{4}$ .

$- (x^{2} - x + \frac{x^{2} \cdot - 7}{x^{2} x^{2}} + \frac{9}{x^{4}})$

Step 16.2.2

Cancel the common factor.

$- (x^{2} - x + \frac{x^{2} \cdot - 7}{x^{2} x^{2}} + \frac{9}{x^{4}})$

Step 16.2.3

Rewrite the expression.

$- (x^{2} - x + \frac{- 7}{x^{2}} + \frac{9}{x^{4}})$

Step 17

Move the negative in front of the fraction.

$- (x^{2} - x - \frac{7}{x^{2}} + \frac{9}{x^{4}})$