Solve (4/7+12/7-9/7)/(5/4-7/3)

$$( 4 / 7 + 12 / 7 - 9 / 7 ) / ( 5 / 4 - 7 / 3 )$$

Evaluate

$$-\frac{12}{13}\approx -0.923076923$$

Solution Steps

Since \frac{4}{7} and \frac{12}{7} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+12}{7}-\frac{9}{7}}{\frac{5}{4}-\frac{7}{3}}$$

Add 4 and 12 to get 16.

$$\frac{\frac{16}{7}-\frac{9}{7}}{\frac{5}{4}-\frac{7}{3}}$$

Since \frac{16}{7} and \frac{9}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16-9}{7}}{\frac{5}{4}-\frac{7}{3}}$$

Subtract 9 from 16 to get 7.

$$\frac{\frac{7}{7}}{\frac{5}{4}-\frac{7}{3}}$$

Divide 7 by 7 to get 1.

$$\frac{1}{\frac{5}{4}-\frac{7}{3}}$$

Least common multiple of 4 and 3 is 12. Convert \frac{5}{4} and \frac{7}{3} to fractions with denominator 12.

$$\frac{1}{\frac{15}{12}-\frac{28}{12}}$$

Since \frac{15}{12} and \frac{28}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{15-28}{12}}$$

Subtract 28 from 15 to get -13.

$$\frac{1}{-\frac{13}{12}}$$

Divide 1 by -\frac{13}{12} by multiplying 1 by the reciprocal of -\frac{13}{12}.

$$1\left(-\frac{12}{13}\right)$$

Multiply 1 and -\frac{12}{13} to get -\frac{12}{13}.

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

Factor

$$-\frac{12}{13} = -0.9230769230769231$$