Pre-Algebra Examples

$\frac{12 x^{4} - 8 x^{3} + 11}{- 12 x^{4}}$

Step 1

Move the negative in front of the fraction.

$- \frac{12 x^{4} - 8 x^{3} + 11}{12 x^{4}}$

Step 2

Split the fraction $\frac{12 x^{4} - 8 x^{3} + 11}{12 x^{4}}$ into two fractions.

$- (\frac{12 x^{4} - 8 x^{3}}{12 x^{4}} + \frac{11}{12 x^{4}})$

Step 3

Split the fraction $\frac{12 x^{4} - 8 x^{3}}{12 x^{4}}$ into two fractions.

$- (\frac{12 x^{4}}{12 x^{4}} + \frac{- 8 x^{3}}{12 x^{4}} + \frac{11}{12 x^{4}})$

Step 4

Cancel the common factor of $12$ .

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Step 4.1

Cancel the common factor.

$- (\frac{12 x^{4}}{12 x^{4}} + \frac{- 8 x^{3}}{12 x^{4}} + \frac{11}{12 x^{4}})$

Step 4.2

Rewrite the expression.

$- (\frac{x^{4}}{x^{4}} + \frac{- 8 x^{3}}{12 x^{4}} + \frac{11}{12 x^{4}})$

Step 5

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

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Step 5.1

Cancel the common factor.

$- (\frac{x^{4}}{x^{4}} + \frac{- 8 x^{3}}{12 x^{4}} + \frac{11}{12 x^{4}})$

Step 5.2

Rewrite the expression.

$- (1 + \frac{- 8 x^{3}}{12 x^{4}} + \frac{11}{12 x^{4}})$

Step 6

Cancel the common factor of $- 8$ and $12$ .

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Step 6.1

Factor $4$ out of $- 8 x^{3}$ .

$- (1 + \frac{4 (- 2 x^{3})}{12 x^{4}} + \frac{11}{12 x^{4}})$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $12 x^{4}$ .

$- (1 + \frac{4 (- 2 x^{3})}{4 (3 x^{4})} + \frac{11}{12 x^{4}})$

Step 6.2.2

Cancel the common factor.

$- (1 + \frac{4 (- 2 x^{3})}{4 (3 x^{4})} + \frac{11}{12 x^{4}})$

Step 6.2.3

Rewrite the expression.

$- (1 + \frac{- 2 x^{3}}{3 x^{4}} + \frac{11}{12 x^{4}})$

Step 7

Cancel the common factor of $x^{3}$ and $x^{4}$ .

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Step 7.1

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

$- (1 + \frac{x^{3} \cdot - 2}{3 x^{4}} + \frac{11}{12 x^{4}})$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$- (1 + \frac{x^{3} \cdot - 2}{x^{3} (3 x)} + \frac{11}{12 x^{4}})$

Step 7.2.2

Cancel the common factor.

$- (1 + \frac{x^{3} \cdot - 2}{x^{3} (3 x)} + \frac{11}{12 x^{4}})$

Step 7.2.3

Rewrite the expression.

$- (1 + \frac{- 2}{3 x} + \frac{11}{12 x^{4}})$

Step 8

Move the negative in front of the fraction.

$- (1 - \frac{2}{3 x} + \frac{11}{12 x^{4}})$