Solve 3/2+4/5/frac{3{2}-4/5}

$$\frac { \frac { 3 } { 2 } + \frac { 4 } { 5 } } { \frac { 3 } { 2 } - \frac { 4 } { 5 } }$$

Evaluate

$$\frac{23}{7}\approx 3.285714286$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{4}{5} to fractions with denominator 10.

$$\frac{\frac{15}{10}+\frac{8}{10}}{\frac{3}{2}-\frac{4}{5}}$$

Since \frac{15}{10} and \frac{8}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15+8}{10}}{\frac{3}{2}-\frac{4}{5}}$$

Add 15 and 8 to get 23.

$$\frac{\frac{23}{10}}{\frac{3}{2}-\frac{4}{5}}$$

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{4}{5} to fractions with denominator 10.

$$\frac{\frac{23}{10}}{\frac{15}{10}-\frac{8}{10}}$$

Since \frac{15}{10} and \frac{8}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23}{10}}{\frac{15-8}{10}}$$

Subtract 8 from 15 to get 7.

$$\frac{\frac{23}{10}}{\frac{7}{10}}$$

Divide \frac{23}{10} by \frac{7}{10} by multiplying \frac{23}{10} by the reciprocal of \frac{7}{10}.

$$\frac{23}{10}\times \frac{10}{7}$$

Multiply \frac{23}{10} times \frac{10}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{23\times 10}{10\times 7}$$

Cancel out 10 in both numerator and denominator.

$$\frac{23}{7}$$

Factor

$$\frac{23}{7} = 3\frac{2}{7} = 3.2857142857142856$$