Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Raise $x$ to the power of $1$ .

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

Step 2.3

Raise $x$ to the power of $1$ .

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

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.5

Add $1$ and $1$ .

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