Pre-Algebra Examples

$\frac{4 x^{9} + 24 x^{7} - 28 x^{2}}{- 4 x^{6}}$

Step 1

Factor $4 x^{2}$ out of $4 x^{9} + 24 x^{7} - 28 x^{2}$ .

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Step 1.1

Factor $4 x^{2}$ out of $4 x^{9}$ .

$\frac{4 x^{2} (x^{7}) + 24 x^{7} - 28 x^{2}}{- 4 x^{6}}$

Step 1.2

Factor $4 x^{2}$ out of $24 x^{7}$ .

$\frac{4 x^{2} (x^{7}) + 4 x^{2} (6 x^{5}) - 28 x^{2}}{- 4 x^{6}}$

Step 1.3

Factor $4 x^{2}$ out of $- 28 x^{2}$ .

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

Step 1.4

Factor $4 x^{2}$ out of $4 x^{2} (x^{7}) + 4 x^{2} (6 x^{5})$ .

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

Step 1.5

Factor $4 x^{2}$ out of $4 x^{2} (x^{7} + 6 x^{5}) + 4 x^{2} (- 7)$ .

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

Step 2

Cancel the common factor of $4$ and $- 4$ .

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Step 2.1

Factor $4$ out of $4 x^{2} (x^{7} + 6 x^{5} - 7)$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factors.

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Step 3.1

Factor $x^{2}$ out of $- x^{6}$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

Move the negative in front of the fraction.

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

Step 5

Split the fraction $\frac{x^{7} + 6 x^{5} - 7}{x^{4}}$ into two fractions.

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

Step 6

Split the fraction $\frac{x^{7} + 6 x^{5}}{x^{4}}$ into two fractions.

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

Step 7

Cancel the common factor of $x^{7}$ and $x^{4}$ .

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Step 7.1

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

$- (\frac{x^{4} x^{3}}{x^{4}} + \frac{6 x^{5}}{x^{4}} + \frac{- 7}{x^{4}})$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Multiply by $1$ .

$- (\frac{x^{4} x^{3}}{x^{4} \cdot 1} + \frac{6 x^{5}}{x^{4}} + \frac{- 7}{x^{4}})$

Step 7.2.2

Cancel the common factor.

$- (\frac{x^{4} x^{3}}{x^{4} \cdot 1} + \frac{6 x^{5}}{x^{4}} + \frac{- 7}{x^{4}})$

Step 7.2.3

Rewrite the expression.

$- (\frac{x^{3}}{1} + \frac{6 x^{5}}{x^{4}} + \frac{- 7}{x^{4}})$

Step 7.2.4

Divide $x^{3}$ by $1$ .

$- (x^{3} + \frac{6 x^{5}}{x^{4}} + \frac{- 7}{x^{4}})$

Step 8

Cancel the common factor of $x^{5}$ and $x^{4}$ .

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Step 8.1

Factor $x^{4}$ out of $6 x^{5}$ .

$- (x^{3} + \frac{x^{4} (6 x)}{x^{4}} + \frac{- 7}{x^{4}})$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Multiply by $1$ .

$- (x^{3} + \frac{x^{4} (6 x)}{x^{4} \cdot 1} + \frac{- 7}{x^{4}})$

Step 8.2.2

Cancel the common factor.

$- (x^{3} + \frac{x^{4} (6 x)}{x^{4} \cdot 1} + \frac{- 7}{x^{4}})$

Step 8.2.3

Rewrite the expression.

$- (x^{3} + \frac{6 x}{1} + \frac{- 7}{x^{4}})$

Step 8.2.4

Divide $6 x$ by $1$ .

$- (x^{3} + 6 x + \frac{- 7}{x^{4}})$

Step 9

Move the negative in front of the fraction.

$- (x^{3} + 6 x - \frac{7}{x^{4}})$