Pre-Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Factor $2 x$ out of $2 x (x) + 2 x (- 1)$ .

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

Step 3

Cancel the common factor of $x - 1$ .

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Step 3.1

Factor $x - 1$ out of $2 x (x - 1)$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

Factor $x$ out of $2 x$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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

Step 6

Apply the distributive property.

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

Step 7

Multiply $3$ by $2$ .

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

Step 8

Multiply $2$ by $- 2$ .

$\frac{6 x - 4}{3 x}$

Step 9

Split the fraction $\frac{6 x - 4}{3 x}$ into two fractions.

$\frac{6 x}{3 x} + \frac{- 4}{3 x}$

Step 10

Cancel the common factor of $6$ and $3$ .

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Step 10.1

Factor $3$ out of $6 x$ .

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

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $3$ out of $3 x$ .

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

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

Step 11

Cancel the common factor of $x$ .

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Step 11.1

Cancel the common factor.

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

Step 11.2

Divide $2$ by $1$ .

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

Step 12

Move the negative in front of the fraction.

$2 - \frac{4}{3 x}$