Solve 5/6+1/4/frac{5{6}-1/4}

$$\frac { \frac { 5 } { 6 } + \frac { 1 } { 4 } } { \frac { 5 } { 6 } - \frac { 1 } { 4 } }$$

Evaluate

$$\frac{13}{7}\approx 1.857142857$$

Solution Steps

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{10}{12}+\frac{3}{12}}{\frac{5}{6}-\frac{1}{4}}$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+3}{12}}{\frac{5}{6}-\frac{1}{4}}$$

Add 10 and 3 to get 13.

$$\frac{\frac{13}{12}}{\frac{5}{6}-\frac{1}{4}}$$

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{13}{12}}{\frac{10}{12}-\frac{3}{12}}$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{12}}{\frac{10-3}{12}}$$

Subtract 3 from 10 to get 7.

$$\frac{\frac{13}{12}}{\frac{7}{12}}$$

Divide \frac{13}{12} by \frac{7}{12} by multiplying \frac{13}{12} by the reciprocal of \frac{7}{12}.

$$\frac{13}{12}\times \frac{12}{7}$$

Multiply \frac{13}{12} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 12}{12\times 7}$$

Cancel out 12 in both numerator and denominator.

$$\frac{13}{7}$$

Factor

$$\frac{13}{7} = 1\frac{6}{7} = 1.8571428571428572$$