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

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

Step 1

Multiply the numerator and denominator of the complex fraction by $x \cdot 3$ .

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Factor $x$ out of $x \cdot 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $3$ .

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

Cancel the common factor of $3 x$ .

Move the leading negative in $- \frac{2}{3 x}$ into the numerator.

$\frac{x \cdot 3 \cdot 2 + 9}{x \cdot 3 \cdot 4 + x \cdot 3 \frac{- 2}{3 x}}$

Factor $3 x$ out of $x \cdot 3$ .

$\frac{x \cdot 3 \cdot 2 + 9}{x \cdot 3 \cdot 4 + 3 \cdot x (1) \frac{- 2}{3 x}}$

Cancel the common factor.

$\frac{x \cdot 3 \cdot 2 + 9}{x \cdot 3 \cdot 4 + 3 \cdot x \cdot 1 \frac{- 2}{3 x}}$

Rewrite the expression.

$\frac{x \cdot 3 \cdot 2 + 9}{x \cdot 3 \cdot 4 - 2}$

Step 4

Simplify the numerator.

Factor $3$ out of $x \cdot 3 \cdot 2 + 9$ .

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

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

Factor $3$ out of $9$ .

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

Factor $3$ out of $3 (x \cdot 2) + 3 \cdot 3$ .

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

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

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

Step 5

Simplify the denominator.

Factor $2$ out of $x \cdot 3 \cdot 4 - 2$ .

Factor $2$ out of $x \cdot 3 \cdot 4$ .

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

Factor $2$ out of $- 2$ .

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

Factor $2$ out of $2 (x \cdot 3 \cdot 2) + 2 (- 1)$ .

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

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

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

Multiply $2$ by $3$ .

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

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

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