Simplify 1/(1/x-4)

$\frac{1}{\frac{1}{x} - 4}$

Simplify the denominator.

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{1}{\frac{1}{x} - 4 \cdot \frac{x}{x}}$

Combine $- 4$ and $\frac{x}{x}$ .

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

Combine the numerators over the common denominator.

$\frac{1}{\frac{1 - 4 x}{x}}$

Multiply the numerator by the reciprocal of the denominator.

$1 \frac{x}{1 - 4 x}$

Multiply $\frac{x}{1 - 4 x}$ by $1$ .

$\frac{x}{1 - 4 x}$