Solve 1+1/1-1{1+frac{1/1-frac{1{3}}}}

$$1 + \frac { 1 } { 1 - \frac { 1 } { 1 + \frac { 1 } { 1 - \frac { 1 } { 3 } } } }$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

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

$$1+\frac{1}{1-\frac{1}{1+\frac{1}{\frac{3}{3}-\frac{1}{3}}}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$1+\frac{1}{1-\frac{1}{1+\frac{1}{\frac{3-1}{3}}}}$$

Subtract 1 from 3 to get 2.

$$1+\frac{1}{1-\frac{1}{1+\frac{1}{\frac{2}{3}}}}$$

Divide 1 by \frac{2}{3} by multiplying 1 by the reciprocal of \frac{2}{3}.

$$1+\frac{1}{1-\frac{1}{1+1\times \frac{3}{2}}}$$

Multiply 1 and \frac{3}{2} to get \frac{3}{2}.

$$1+\frac{1}{1-\frac{1}{1+\frac{3}{2}}}$$

Convert 1 to fraction \frac{2}{2}.

$$1+\frac{1}{1-\frac{1}{\frac{2}{2}+\frac{3}{2}}}$$

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

$$1+\frac{1}{1-\frac{1}{\frac{2+3}{2}}}$$

Add 2 and 3 to get 5.

$$1+\frac{1}{1-\frac{1}{\frac{5}{2}}}$$

Divide 1 by \frac{5}{2} by multiplying 1 by the reciprocal of \frac{5}{2}.

$$1+\frac{1}{1-1\times \frac{2}{5}}$$

Multiply 1 and \frac{2}{5} to get \frac{2}{5}.

$$1+\frac{1}{1-\frac{2}{5}}$$

Convert 1 to fraction \frac{5}{5}.

$$1+\frac{1}{\frac{5}{5}-\frac{2}{5}}$$

Since \frac{5}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$1+\frac{1}{\frac{5-2}{5}}$$

Subtract 2 from 5 to get 3.

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

Divide 1 by \frac{3}{5} by multiplying 1 by the reciprocal of \frac{3}{5}.

$$1+1\times \frac{5}{3}$$

Multiply 1 and \frac{5}{3} to get \frac{5}{3}.

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

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

$$\frac{3}{3}+\frac{5}{3}$$

Since \frac{3}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

$$\frac{3+5}{3}$$

Add 3 and 5 to get 8.

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$