Algebra Examples

$\frac{3 x - 6}{x^{3}} \div \frac{x - 2}{2 x - 1}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 x - 6}{x^{3}} \cdot \frac{2 x - 1}{x - 2}$

Step 2

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

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Step 2.1

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{x^{3}} \cdot \frac{2 x - 1}{x - 2}$

Step 2.2

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{x^{3}} \cdot \frac{2 x - 1}{x - 2}$

Step 2.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{3 (x - 2)}{x^{3}} \cdot \frac{2 x - 1}{x - 2}$

Step 3

Cancel the common factor of $x - 2$ .

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Step 3.1

Factor $x - 2$ out of $3 (x - 2)$ .

$\frac{(x - 2) \cdot 3}{x^{3}} \cdot \frac{2 x - 1}{x - 2}$

Step 3.2

Cancel the common factor.

$\frac{(x - 2) \cdot 3}{x^{3}} \cdot \frac{2 x - 1}{x - 2}$

Step 3.3

Rewrite the expression.

$\frac{3}{x^{3}} (2 x - 1)$

Step 4

Multiply $\frac{3}{x^{3}}$ by $2 x - 1$ .

$\frac{3 (2 x - 1)}{x^{3}}$

Step 5

Apply the distributive property.

$\frac{3 (2 x) + 3 \cdot - 1}{x^{3}}$

Step 6

Multiply $2$ by $3$ .

$\frac{6 x + 3 \cdot - 1}{x^{3}}$

Step 7

Multiply $3$ by $- 1$ .

$\frac{6 x - 3}{x^{3}}$

Step 8

Split the fraction $\frac{6 x - 3}{x^{3}}$ into two fractions.

$\frac{6 x}{x^{3}} + \frac{- 3}{x^{3}}$

Step 9

Cancel the common factor of $x$ and $x^{3}$ .

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Step 9.1

Factor $x$ out of $6 x$ .

$\frac{x \cdot 6}{x^{3}} + \frac{- 3}{x^{3}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

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

$\frac{x \cdot 6}{x \cdot x^{2}} + \frac{- 3}{x^{3}}$

Step 9.2.2

Cancel the common factor.

$\frac{x \cdot 6}{x \cdot x^{2}} + \frac{- 3}{x^{3}}$

Step 9.2.3

Rewrite the expression.

$\frac{6}{x^{2}} + \frac{- 3}{x^{3}}$

Step 10

Move the negative in front of the fraction.

$\frac{6}{x^{2}} - \frac{3}{x^{3}}$