Pre-Algebra Examples

$\frac{- 40 x^{6} - 48 x^{5} - 48 x^{4}}{- 8 x^{5}}$

Step 1

Factor $8 x^{4}$ out of $- 40 x^{6} - 48 x^{5} - 48 x^{4}$ .

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Step 1.1

Factor $8 x^{4}$ out of $- 40 x^{6}$ .

$\frac{8 x^{4} (- 5 x^{2}) - 48 x^{5} - 48 x^{4}}{- 8 x^{5}}$

Step 1.2

Factor $8 x^{4}$ out of $- 48 x^{5}$ .

$\frac{8 x^{4} (- 5 x^{2}) + 8 x^{4} (- 6 x) - 48 x^{4}}{- 8 x^{5}}$

Step 1.3

Factor $8 x^{4}$ out of $- 48 x^{4}$ .

$\frac{8 x^{4} (- 5 x^{2}) + 8 x^{4} (- 6 x) + 8 x^{4} (- 6)}{- 8 x^{5}}$

Step 1.4

Factor $8 x^{4}$ out of $8 x^{4} (- 5 x^{2}) + 8 x^{4} (- 6 x)$ .

$\frac{8 x^{4} (- 5 x^{2} - 6 x) + 8 x^{4} (- 6)}{- 8 x^{5}}$

Step 1.5

Factor $8 x^{4}$ out of $8 x^{4} (- 5 x^{2} - 6 x) + 8 x^{4} (- 6)$ .

$\frac{8 x^{4} (- 5 x^{2} - 6 x - 6)}{- 8 x^{5}}$

Step 2

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

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Step 2.1

Factor $8$ out of $8 x^{4} (- 5 x^{2} - 6 x - 6)$ .

$\frac{8 (x^{4} (- 5 x^{2} - 6 x - 6))}{- 8 x^{5}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $8$ out of $- 8 x^{5}$ .

$\frac{8 (x^{4} (- 5 x^{2} - 6 x - 6))}{8 (- x^{5})}$

Step 2.2.2

Cancel the common factor.

$\frac{8 (x^{4} (- 5 x^{2} - 6 x - 6))}{8 (- x^{5})}$

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factors.

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Step 3.1

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

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

$\frac{- 5 x^{2} - 6 x - 6}{- x}$

Step 4

Move the negative in front of the fraction.

$- \frac{- 5 x^{2} - 6 x - 6}{x}$

Step 5

Factor $- 1$ out of $- 5 x^{2}$ .

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

Step 6

Factor $- 1$ out of $- 6 x$ .

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

Step 7

Factor $- 1$ out of $- (5 x^{2}) - (6 x)$ .

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

Step 8

Rewrite $- 6$ as $- 1 (6)$ .

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

Step 9

Factor $- 1$ out of $- (5 x^{2} + 6 x) - 1 (6)$ .

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

Step 10

Simplify the expression.

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Step 10.1

Rewrite $- (5 x^{2} + 6 x + 6)$ as $- 1 (5 x^{2} + 6 x + 6)$ .

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

Step 10.2

Move the negative in front of the fraction.

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

Step 10.3

Multiply $- 1$ by $- 1$ .

$1 \frac{5 x^{2} + 6 x + 6}{x}$

Step 10.4

Multiply $\frac{5 x^{2} + 6 x + 6}{x}$ by $1$ .

$\frac{5 x^{2} + 6 x + 6}{x}$