Algebra Examples

$\frac{3 x^{5} - 15 x^{3} + 6 x}{9 x}$

Step 1

Factor $3 x$ out of $3 x^{5} - 15 x^{3} + 6 x$ .

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Step 1.1

Factor $3 x$ out of $3 x^{5}$ .

$\frac{3 x (x^{4}) - 15 x^{3} + 6 x}{9 x}$

Step 1.2

Factor $3 x$ out of $- 15 x^{3}$ .

$\frac{3 x (x^{4}) + 3 x (- 5 x^{2}) + 6 x}{9 x}$

Step 1.3

Factor $3 x$ out of $6 x$ .

$\frac{3 x (x^{4}) + 3 x (- 5 x^{2}) + 3 x (2)}{9 x}$

Step 1.4

Factor $3 x$ out of $3 x (x^{4}) + 3 x (- 5 x^{2})$ .

$\frac{3 x (x^{4} - 5 x^{2}) + 3 x (2)}{9 x}$

Step 1.5

Factor $3 x$ out of $3 x (x^{4} - 5 x^{2}) + 3 x (2)$ .

$\frac{3 x (x^{4} - 5 x^{2} + 2)}{9 x}$

Step 2

Cancel the common factor of $3$ and $9$ .

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Step 2.1

Factor $3$ out of $3 x (x^{4} - 5 x^{2} + 2)$ .

$\frac{3 (x (x^{4} - 5 x^{2} + 2))}{9 x}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $9 x$ .

$\frac{3 (x (x^{4} - 5 x^{2} + 2))}{3 (3 x)}$

Step 2.2.2

Cancel the common factor.

$\frac{3 (x (x^{4} - 5 x^{2} + 2))}{3 (3 x)}$

Step 2.2.3

Rewrite the expression.

$\frac{x (x^{4} - 5 x^{2} + 2)}{3 x}$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\frac{x (x^{4} - 5 x^{2} + 2)}{3 x}$

Step 3.2

Rewrite the expression.

$\frac{x^{4} - 5 x^{2} + 2}{3}$

Step 4

Split the fraction $\frac{x^{4} - 5 x^{2} + 2}{3}$ into two fractions.

$\frac{x^{4} - 5 x^{2}}{3} + \frac{2}{3}$

Step 5

Split the fraction $\frac{x^{4} - 5 x^{2}}{3}$ into two fractions.

$\frac{x^{4}}{3} + \frac{- 5 x^{2}}{3} + \frac{2}{3}$

Step 6

Move the negative in front of the fraction.

$\frac{x^{4}}{3} - \frac{5 x^{2}}{3} + \frac{2}{3}$