Pre-Algebra Examples

$\frac{10 x^{3} - 24 x^{2} - 10 x}{10 x}$

Step 1

Factor $2 x$ out of $10 x^{3} - 24 x^{2} - 10 x$ .

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Step 1.1

Factor $2 x$ out of $10 x^{3}$ .

$\frac{2 x (5 x^{2}) - 24 x^{2} - 10 x}{10 x}$

Step 1.2

Factor $2 x$ out of $- 24 x^{2}$ .

$\frac{2 x (5 x^{2}) + 2 x (- 12 x) - 10 x}{10 x}$

Step 1.3

Factor $2 x$ out of $- 10 x$ .

$\frac{2 x (5 x^{2}) + 2 x (- 12 x) + 2 x (- 5)}{10 x}$

Step 1.4

Factor $2 x$ out of $2 x (5 x^{2}) + 2 x (- 12 x)$ .

$\frac{2 x (5 x^{2} - 12 x) + 2 x (- 5)}{10 x}$

Step 1.5

Factor $2 x$ out of $2 x (5 x^{2} - 12 x) + 2 x (- 5)$ .

$\frac{2 x (5 x^{2} - 12 x - 5)}{10 x}$

Step 2

Cancel the common factor of $2$ and $10$ .

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Step 2.1

Factor $2$ out of $2 x (5 x^{2} - 12 x - 5)$ .

$\frac{2 (x (5 x^{2} - 12 x - 5))}{10 x}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $10 x$ .

$\frac{2 (x (5 x^{2} - 12 x - 5))}{2 (5 x)}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (x (5 x^{2} - 12 x - 5))}{2 (5 x)}$

Step 2.2.3

Rewrite the expression.

$\frac{x (5 x^{2} - 12 x - 5)}{5 x}$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\frac{x (5 x^{2} - 12 x - 5)}{5 x}$

Step 3.2

Rewrite the expression.

$\frac{5 x^{2} - 12 x - 5}{5}$

Step 4

Split the fraction $\frac{5 x^{2} - 12 x - 5}{5}$ into two fractions.

$\frac{5 x^{2} - 12 x}{5} + \frac{- 5}{5}$

Step 5

Split the fraction $\frac{5 x^{2} - 12 x}{5}$ into two fractions.

$\frac{5 x^{2}}{5} + \frac{- 12 x}{5} + \frac{- 5}{5}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Cancel the common factor.

$\frac{5 x^{2}}{5} + \frac{- 12 x}{5} + \frac{- 5}{5}$

Step 6.2

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{- 12 x}{5} + \frac{- 5}{5}$

Step 7

Move the negative in front of the fraction.

$x^{2} - \frac{12 x}{5} + \frac{- 5}{5}$

Step 8

Divide $- 5$ by $5$ .

$x^{2} - \frac{12 x}{5} - 1$