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

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

Verify

Solution Steps

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

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

Since \frac{6}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

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

Add 6 and 1 to get 7.

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

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

$$\frac{\frac{7}{3}}{\frac{6}{3}-\frac{1}{3}}=\frac{\frac{1}{2}+\frac{1}{3}}{\frac{1}{2}-\frac{1}{3}}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{3}}{\frac{6-1}{3}}=\frac{\frac{1}{2}+\frac{1}{3}}{\frac{1}{2}-\frac{1}{3}}$$

Subtract 1 from 6 to get 5.

$$\frac{\frac{7}{3}}{\frac{5}{3}}=\frac{\frac{1}{2}+\frac{1}{3}}{\frac{1}{2}-\frac{1}{3}}$$

Divide \frac{7}{3} by \frac{5}{3} by multiplying \frac{7}{3} by the reciprocal of \frac{5}{3}.

$$\frac{7}{3}\times \frac{3}{5}=\frac{\frac{1}{2}+\frac{1}{3}}{\frac{1}{2}-\frac{1}{3}}$$

Multiply \frac{7}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 3}{3\times 5}=\frac{\frac{1}{2}+\frac{1}{3}}{\frac{1}{2}-\frac{1}{3}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{7}{5}=\frac{\frac{1}{2}+\frac{1}{3}}{\frac{1}{2}-\frac{1}{3}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{7}{5}=\frac{\frac{3}{6}+\frac{2}{6}}{\frac{1}{2}-\frac{1}{3}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{7}{5}=\frac{\frac{3+2}{6}}{\frac{1}{2}-\frac{1}{3}}$$

Add 3 and 2 to get 5.

$$\frac{7}{5}=\frac{\frac{5}{6}}{\frac{1}{2}-\frac{1}{3}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{7}{5}=\frac{\frac{5}{6}}{\frac{3}{6}-\frac{2}{6}}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{5}=\frac{\frac{5}{6}}{\frac{3-2}{6}}$$

Subtract 2 from 3 to get 1.

$$\frac{7}{5}=\frac{\frac{5}{6}}{\frac{1}{6}}$$

Divide \frac{5}{6} by \frac{1}{6} by multiplying \frac{5}{6} by the reciprocal of \frac{1}{6}.

$$\frac{7}{5}=\frac{5}{6}\times 6$$

Cancel out 6 and 6.

$$\frac{7}{5}=5$$

Convert 5 to fraction \frac{25}{5}.

$$\frac{7}{5}=\frac{25}{5}$$

Compare \frac{7}{5} and \frac{25}{5}.

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