Pre-Algebra Examples

$\frac{- 49 x^{7} - 49 x^{6} - 14 x^{5}}{- 7 x^{6}}$

Step 1

Factor $7 x^{5}$ out of $- 49 x^{7} - 49 x^{6} - 14 x^{5}$ .

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Step 1.1

Factor $7 x^{5}$ out of $- 49 x^{7}$ .

$\frac{7 x^{5} (- 7 x^{2}) - 49 x^{6} - 14 x^{5}}{- 7 x^{6}}$

Step 1.2

Factor $7 x^{5}$ out of $- 49 x^{6}$ .

$\frac{7 x^{5} (- 7 x^{2}) + 7 x^{5} (- 7 x) - 14 x^{5}}{- 7 x^{6}}$

Step 1.3

Factor $7 x^{5}$ out of $- 14 x^{5}$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 2

Cancel the common factor of $7$ and $- 7$ .

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $7$ out of $- 7 x^{6}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factors.

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Step 3.1

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

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

$\frac{- 7 x^{2} - 7 x - 2}{- x}$

Step 4

Move the negative in front of the fraction.

$- \frac{- 7 x^{2} - 7 x - 2}{x}$

Step 5

Factor $- 1$ out of $- 7 x^{2}$ .

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

Step 6

Factor $- 1$ out of $- 7 x$ .

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

Step 7

Factor $- 1$ out of $- (7 x^{2}) - (7 x)$ .

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

Step 8

Rewrite $- 2$ as $- 1 (2)$ .

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

Step 9

Factor $- 1$ out of $- (7 x^{2} + 7 x) - 1 (2)$ .

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

Step 10

Rewrite $- (7 x^{2} + 7 x + 2)$ as $- 1 (7 x^{2} + 7 x + 2)$ .

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

Step 11

Move the negative in front of the fraction.

$- - \frac{7 x^{2} + 7 x + 2}{x}$

Step 12

Multiply $- 1$ by $- 1$ .

$1 \frac{7 x^{2} + 7 x + 2}{x}$

Step 13

Multiply $\frac{7 x^{2} + 7 x + 2}{x}$ by $1$ .

$\frac{7 x^{2} + 7 x + 2}{x}$

Step 14

Split the fraction $\frac{7 x^{2} + 7 x + 2}{x}$ into two fractions.

$\frac{7 x^{2} + 7 x}{x} + \frac{2}{x}$

Step 15

Split the fraction $\frac{7 x^{2} + 7 x}{x}$ into two fractions.

$\frac{7 x^{2}}{x} + \frac{7 x}{x} + \frac{2}{x}$

Step 16

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

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Step 16.1

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

$\frac{x (7 x)}{x} + \frac{7 x}{x} + \frac{2}{x}$

Step 16.2

Cancel the common factors.

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Step 16.2.1

Raise $x$ to the power of $1$ .

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

Step 16.2.2

Factor $x$ out of $x^{1}$ .

$\frac{x (7 x)}{x \cdot 1} + \frac{7 x}{x} + \frac{2}{x}$

Step 16.2.3

Cancel the common factor.

$\frac{x (7 x)}{x \cdot 1} + \frac{7 x}{x} + \frac{2}{x}$

Step 16.2.4

Rewrite the expression.

$\frac{7 x}{1} + \frac{7 x}{x} + \frac{2}{x}$

Step 16.2.5

Divide $7 x$ by $1$ .

$7 x + \frac{7 x}{x} + \frac{2}{x}$

Step 17

Cancel the common factor of $x$ .

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Step 17.1

Cancel the common factor.

$7 x + \frac{7 x}{x} + \frac{2}{x}$

Step 17.2

Divide $7$ by $1$ .

$7 x + 7 + \frac{2}{x}$