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

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

Evaluate

$$2$$

Solution Steps

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

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

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

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

Subtract 1 from 2 to get 1.

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

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

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

Multiply 3 and 2 to get 6.

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

Add -1 and 6 to get 5.

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

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

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

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

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

Add 2 and 1 to get 3.

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

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

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

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

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

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

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

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

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

Add 3 and 2 to get 5.

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

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

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

Express 3\times \frac{3}{5} as a single fraction.

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

Multiply 3 and 3 to get 9.

$$\frac{1}{5}+\frac{9}{5}$$

Since \frac{1}{5} and \frac{9}{5} have the same denominator, add them by adding their numerators.

$$\frac{1+9}{5}$$

Add 1 and 9 to get 10.

$$\frac{10}{5}$$

Divide 10 by 5 to get 2.

$$2$$

Factor

$$2$$