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

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Simplify the denominator.

To write $3$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

Combine the numerators over the common denominator.

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

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

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

Step 5

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

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