Solve 1+frac{1/1+frac{1{2}}}{1-1/1+frac{1{2}}}

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

Evaluate

$$5$$

Solution Steps

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

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

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

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

Add 2 and 1 to get 3.

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

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

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

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

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

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

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

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

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

Add 3 and 2 to get 5.

$$\frac{\frac{5}{3}}{1-\frac{1}{1+\frac{1}{2}}}$$

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

$$\frac{\frac{5}{3}}{1-\frac{1}{\frac{2}{2}+\frac{1}{2}}}$$

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

$$\frac{\frac{5}{3}}{1-\frac{1}{\frac{2+1}{2}}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{5}{3}}{1-\frac{1}{\frac{3}{2}}}$$

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

$$\frac{\frac{5}{3}}{1-1\times \frac{2}{3}}$$

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

$$\frac{\frac{5}{3}}{1-\frac{2}{3}}$$

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

$$\frac{\frac{5}{3}}{\frac{3}{3}-\frac{2}{3}}$$

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

$$\frac{\frac{5}{3}}{\frac{3-2}{3}}$$

Subtract 2 from 3 to get 1.

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

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

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

Cancel out 3 and 3.

$$5$$

Factor

$$5$$