Solve 1/1-(1-1{1-frac{2/3})}

$$\frac { 1 } { 1 - ( 1 - \frac { 1 } { 1 - \frac { 2 } { 3 } } ) }$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

$$\frac{1}{1-\left(1-\frac{1}{\frac{3}{3}-\frac{2}{3}}\right)}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{1-\left(1-\frac{1}{\frac{3-2}{3}}\right)}$$

Subtract 2 from 3 to get 1.

$$\frac{1}{1-\left(1-\frac{1}{\frac{1}{3}}\right)}$$

Divide 1 by \frac{1}{3} by multiplying 1 by the reciprocal of \frac{1}{3}.

$$\frac{1}{1-\left(1-1\times 3\right)}$$

Multiply 1 and 3 to get 3.

$$\frac{1}{1-\left(1-3\right)}$$

Subtract 3 from 1 to get -2.

$$\frac{1}{1-\left(-2\right)}$$

The opposite of -2 is 2.

$$\frac{1}{1+2}$$

Add 1 and 2 to get 3.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$