Solve 1(1-1/1-frac{1{x}})=20191

$$1 ( 1 - \frac { 1 } { 1 - \frac { 1 } { x } } ) = 20191$$

Solve for x

$$x=\frac{20190}{20191}\approx 0.999950473$$

Steps for Solving Linear Equation

Divide both sides by 1.

$$1-\frac{1}{1-\frac{1}{x}}=20191$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

$$1-\frac{1}{\frac{x}{x}-\frac{1}{x}}=20191$$

Since \frac{x}{x} and \frac{1}{x} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{1}{\frac{x-1}{x}}=20191$$

Variable x cannot be equal to 0 since division by zero is not defined. Divide 1 by \frac{x-1}{x} by multiplying 1 by the reciprocal of \frac{x-1}{x}.

$$1-\frac{x}{x-1}=20191$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-1}{x-1}.

$$\frac{x-1}{x-1}-\frac{x}{x-1}=20191$$

Since \frac{x-1}{x-1} and \frac{x}{x-1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-1-x}{x-1}=20191$$

Combine like terms in x-1-x.

$$\frac{-1}{x-1}=20191$$

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by x-1.

$$-1=20191\left(x-1\right)$$

Divide both sides by 20191.

$$-\frac{1}{20191}=x-1$$

Swap sides so that all variable terms are on the left hand side.

$$x-1=-\frac{1}{20191}$$

Add 1 to both sides.

$$x=-\frac{1}{20191}+1$$

Add -\frac{1}{20191} and 1 to get \frac{20190}{20191}.

$$x=\frac{20190}{20191}$$