Simplify 5/(1/6+1/(x+1))

$\frac{5}{\frac{1}{6} + \frac{1}{x + 1}}$

Simplify the denominator.

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

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

To write $\frac{1}{x + 1}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

Write each expression with a common denominator of $6 (x + 1)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{6}$ by $\frac{x + 1}{x + 1}$ .

$\frac{5}{\frac{x + 1}{6 (x + 1)} + \frac{1}{x + 1} \cdot \frac{6}{6}}$

Multiply $\frac{1}{x + 1}$ by $\frac{6}{6}$ .

$\frac{5}{\frac{x + 1}{6 (x + 1)} + \frac{6}{(x + 1) \cdot 6}}$

Reorder the factors of $(x + 1) \cdot 6$ .

$\frac{5}{\frac{x + 1}{6 (x + 1)} + \frac{6}{6 (x + 1)}}$

Combine the numerators over the common denominator.

$\frac{5}{\frac{x + 1 + 6}{6 (x + 1)}}$

Add $1$ and $6$ .

$\frac{5}{\frac{x + 7}{6 (x + 1)}}$

Multiply the numerator by the reciprocal of the denominator.

$5 \frac{6 (x + 1)}{x + 7}$

Multiply $5 \frac{6 (x + 1)}{x + 7}$ .

Combine $5$ and $\frac{6 (x + 1)}{x + 7}$ .

$\frac{5 (6 (x + 1))}{x + 7}$

Multiply $6$ by $5$ .

$\frac{30 (x + 1)}{x + 7}$