Simplify (1/3+1/(3x))/(1/x+1/3)

$\frac{\frac{1}{3} + \frac{1}{3 x}}{\frac{1}{x} + \frac{1}{3}}$

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

Multiply $\frac{\frac{1}{3} + \frac{1}{3 x}}{\frac{1}{x} + \frac{1}{3}}$ by $\frac{3 x}{3 x}$ .

$\frac{3 x}{3 x} \cdot \frac{\frac{1}{3} + \frac{1}{3 x}}{\frac{1}{x} + \frac{1}{3}}$

Combine.

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

Apply the distributive property.

$\frac{3 x \frac{1}{3} + 3 x \frac{1}{3 x}}{3 x \frac{1}{x} + 3 x \frac{1}{3}}$

Simplify by cancelling.

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

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

Cancel the common factor.

$\frac{3 x \frac{1}{3} + 3 x \frac{1}{3 x}}{3 x \frac{1}{x} + 3 x \frac{1}{3}}$

Rewrite the expression.

$\frac{x + 3 x \frac{1}{3 x}}{3 x \frac{1}{x} + 3 x \frac{1}{3}}$

Cancel the common factor of $3 x$ .

Cancel the common factor.

$\frac{x + 3 x \frac{1}{3 x}}{3 x \frac{1}{x} + 3 x \frac{1}{3}}$

Rewrite the expression.

$\frac{x + 1}{3 x \frac{1}{x} + 3 x \frac{1}{3}}$

Cancel the common factor of $x$ .

Factor $x$ out of $3 x$ .

$\frac{x + 1}{x \cdot 3 \frac{1}{x} + 3 x \frac{1}{3}}$

Cancel the common factor.

$\frac{x + 1}{x \cdot 3 \frac{1}{x} + 3 x \frac{1}{3}}$

Rewrite the expression.

$\frac{x + 1}{3 + 3 x \frac{1}{3}}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

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

Cancel the common factor.

$\frac{x + 1}{3 + 3 x \frac{1}{3}}$

Rewrite the expression.

$\frac{x + 1}{3 + x}$