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

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

Evaluate

$$9$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{3}{5} to fractions with denominator 20.

$$\frac{\frac{15}{20}+\frac{12}{20}}{\frac{3}{4}-\frac{3}{5}}$$

Since \frac{15}{20} and \frac{12}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15+12}{20}}{\frac{3}{4}-\frac{3}{5}}$$

Add 15 and 12 to get 27.

$$\frac{\frac{27}{20}}{\frac{3}{4}-\frac{3}{5}}$$

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{3}{5} to fractions with denominator 20.

$$\frac{\frac{27}{20}}{\frac{15}{20}-\frac{12}{20}}$$

Since \frac{15}{20} and \frac{12}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27}{20}}{\frac{15-12}{20}}$$

Subtract 12 from 15 to get 3.

$$\frac{\frac{27}{20}}{\frac{3}{20}}$$

Divide \frac{27}{20} by \frac{3}{20} by multiplying \frac{27}{20} by the reciprocal of \frac{3}{20}.

$$\frac{27}{20}\times \frac{20}{3}$$

Multiply \frac{27}{20} times \frac{20}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27\times 20}{20\times 3}$$

Cancel out 20 in both numerator and denominator.

$$\frac{27}{3}$$

Divide 27 by 3 to get 9.

$$9$$

Factor

$$3^{2}$$