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

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

Evaluate

$$4$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{\frac{10}{15}+\frac{6}{15}}{\frac{2}{3}-\frac{2}{5}}$$

Since \frac{10}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+6}{15}}{\frac{2}{3}-\frac{2}{5}}$$

Add 10 and 6 to get 16.

$$\frac{\frac{16}{15}}{\frac{2}{3}-\frac{2}{5}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{\frac{16}{15}}{\frac{10}{15}-\frac{6}{15}}$$

Since \frac{10}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16}{15}}{\frac{10-6}{15}}$$

Subtract 6 from 10 to get 4.

$$\frac{\frac{16}{15}}{\frac{4}{15}}$$

Divide \frac{16}{15} by \frac{4}{15} by multiplying \frac{16}{15} by the reciprocal of \frac{4}{15}.

$$\frac{16}{15}\times \frac{15}{4}$$

Multiply \frac{16}{15} times \frac{15}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 15}{15\times 4}$$

Cancel out 15 in both numerator and denominator.

$$\frac{16}{4}$$

Divide 16 by 4 to get 4.

$$4$$

Factor

$$2^{2}$$