Solve 1+frac{1/1-frac{1{2}}}{-1+3/1+frac{1{2}}}

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

Evaluate

$$3$$

Solution Steps

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

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

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

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

Subtract 1 from 2 to get 1.

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

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

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

Multiply 1 and 2 to get 2.

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

Add 1 and 2 to get 3.

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

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

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

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

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

Add 2 and 1 to get 3.

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

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

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

Cancel out 3 and 3.

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

Add -1 and 2 to get 1.

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

Anything divided by one gives itself.

$$3$$

Factor

$$3$$