Solve 1+1/2/1-frac{1{2}}:[1-1/1-frac{1{2}}]=

$$\frac { 1 + \frac { 1 } { 2 } } { 1 - \frac { 1 } { 2 } } : [ 1 - \frac { 1 } { 1 - \frac { 1 } { 2 } } ] =$$

Evaluate

$$-3$$

Solution Steps

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

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

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

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

Add 2 and 1 to get 3.

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

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

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

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

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

Subtract 1 from 2 to get 1.

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

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

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

Cancel out 2 and 2.

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

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

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

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

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

Subtract 1 from 2 to get 1.

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

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

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

Multiply 1 and 2 to get 2.

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

Subtract 2 from 1 to get -1.

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

Fraction \frac{3}{-1} can be rewritten as -3 by extracting the negative sign.

$$-3$$

Factor

$$-3$$