Divide (4+2/x)/(3-2/x)

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

Step 1

Multiply the numerator and denominator of the complex fraction by $x$ .

Multiply $\frac{4 + \frac{2}{x}}{3 - \frac{2}{x}}$ by $\frac{x}{x}$ .

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{2}{x}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the numerator.

Factor $2$ out of $x \cdot 4 + 2$ .

Factor $2$ out of $x \cdot 4$ .

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $2 (x \cdot 2) + 2 (1)$ .

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

Move $2$ to the left of $x$ .

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

Step 5

Move $3$ to the left of $x$ .

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