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

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

Evaluate

$$\frac{23}{7}\approx 3.285714286$$

Solution Steps

Subtract 1 from 3 to get 2.

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

Convert 3 to fraction \frac{6}{2}.

$$3+\frac{1}{\frac{6}{2}+\frac{1}{2}}$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$3+\frac{1}{\frac{6+1}{2}}$$

Add 6 and 1 to get 7.

$$3+\frac{1}{\frac{7}{2}}$$

Divide 1 by \frac{7}{2} by multiplying 1 by the reciprocal of \frac{7}{2}.

$$3+1\times \frac{2}{7}$$

Multiply 1 and \frac{2}{7} to get \frac{2}{7}.

$$3+\frac{2}{7}$$

Convert 3 to fraction \frac{21}{7}.

$$\frac{21}{7}+\frac{2}{7}$$

Since \frac{21}{7} and \frac{2}{7} have the same denominator, add them by adding their numerators.

$$\frac{21+2}{7}$$

Add 21 and 2 to get 23.

$$\frac{23}{7}$$

Factor

$$\frac{23}{7} = 3\frac{2}{7} = 3.2857142857142856$$