Simplify (5/(x+3))/(2+1/(x+3))

$\frac{\frac{5}{x + 3}}{2 + \frac{1}{x + 3}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{x + 3} \cdot \frac{1}{2 + \frac{1}{x + 3}}$

Step 2

Simplify the denominator.

To write $2$ as a fraction with a common denominator, multiply by $\frac{x + 3}{x + 3}$ .

$\frac{5}{x + 3} \cdot \frac{1}{\frac{2 (x + 3)}{x + 3} + \frac{1}{x + 3}}$

Combine the numerators over the common denominator.

$\frac{5}{x + 3} \cdot \frac{1}{\frac{2 (x + 3) + 1}{x + 3}}$

Rewrite $\frac{2 (x + 3) + 1}{x + 3}$ in a factored form.

Apply the distributive property.

$\frac{5}{x + 3} \cdot \frac{1}{\frac{2 x + 2 \cdot 3 + 1}{x + 3}}$

Multiply $2$ by $3$ .

$\frac{5}{x + 3} \cdot \frac{1}{\frac{2 x + 6 + 1}{x + 3}}$

Add $6$ and $1$ .

$\frac{5}{x + 3} \cdot \frac{1}{\frac{2 x + 7}{x + 3}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{x + 3} (1 \frac{x + 3}{2 x + 7})$

Step 4

Multiply $\frac{x + 3}{2 x + 7}$ by $1$ .

$\frac{5}{x + 3} \cdot \frac{x + 3}{2 x + 7}$

Step 5

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{5}{x + 3} \cdot \frac{x + 3}{2 x + 7}$

Rewrite the expression.

$5 \frac{1}{2 x + 7}$

Step 6

Combine $5$ and $\frac{1}{2 x + 7}$ .

$\frac{5}{2 x + 7}$