Simplify (3/x+1/4)/(1+3/x)

$\frac{\frac{3}{x} + \frac{1}{4}}{1 + \frac{3}{x}}$

Multiply the numerator and denominator of the complex fraction by $x \cdot 4$ .

Multiply $\frac{\frac{3}{x} + \frac{1}{4}}{1 + \frac{3}{x}}$ by $\frac{x \cdot 4}{x \cdot 4}$ .

$\frac{x \cdot 4}{x \cdot 4} \cdot \frac{\frac{3}{x} + \frac{1}{4}}{1 + \frac{3}{x}}$

Combine.

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

Apply the distributive property.

$\frac{x \cdot 4 \frac{3}{x} + x \cdot 4 \frac{1}{4}}{x \cdot 4 \cdot 1 + x \cdot 4 \frac{3}{x}}$

Simplify by cancelling.

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

$\frac{x \cdot 4 \frac{3}{x} + x \cdot 4 \frac{1}{4}}{x \cdot 4 \cdot 1 + x \cdot 4 \frac{3}{x}}$

Rewrite the expression.

$\frac{4 \cdot 3 + x \cdot 4 \frac{1}{4}}{x \cdot 4 \cdot 1 + x \cdot 4 \frac{3}{x}}$

Multiply $4$ by $3$ .

$\frac{12 + x \cdot 4 \frac{1}{4}}{x \cdot 4 \cdot 1 + x \cdot 4 \frac{3}{x}}$

Cancel the common factor of $4$ .

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

$\frac{12 + 4 \cdot x \frac{1}{4}}{x \cdot 4 \cdot 1 + x \cdot 4 \frac{3}{x}}$

Cancel the common factor.

$\frac{12 + 4 \cdot x \frac{1}{4}}{x \cdot 4 \cdot 1 + x \cdot 4 \frac{3}{x}}$

Rewrite the expression.

$\frac{12 + x}{x \cdot 4 \cdot 1 + x \cdot 4 \frac{3}{x}}$

Cancel the common factor of $x$ .

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

$\frac{12 + x}{x \cdot 4 \cdot 1 + x (4) \frac{3}{x}}$

Cancel the common factor.

$\frac{12 + x}{x \cdot 4 \cdot 1 + x \cdot 4 \frac{3}{x}}$

Rewrite the expression.

$\frac{12 + x}{x \cdot 4 \cdot 1 + 4 \cdot 3}$

Multiply $4$ by $3$ .

$\frac{12 + x}{x \cdot 4 \cdot 1 + 12}$

Simplify the denominator.

Factor $4$ out of $x \cdot 4 \cdot 1 + 12$ .

Factor $4$ out of $x \cdot 4 \cdot 1$ .

$\frac{12 + x}{4 (x \cdot 1) + 12}$

Factor $4$ out of $12$ .

$\frac{12 + x}{4 (x \cdot 1) + 4 \cdot 3}$

Factor $4$ out of $4 (x \cdot 1) + 4 \cdot 3$ .

$\frac{12 + x}{4 (x \cdot 1 + 3)}$

Multiply $x$ by $1$ .

$\frac{12 + x}{4 (x + 3)}$