Solve 9/7+6/5-15/13/frac{5{12}-frac{3}{7}-frac{2}{5}}

$$\frac { \frac { 9 } { 7 } + \frac { 6 } { 5 } - \frac { 15 } { 13 } } { \frac { 5 } { 12 } - \frac { 3 } { 7 } - \frac { 2 } { 5 } }$$

Evaluate

$$-\frac{7272}{2249}\approx -3.233437083$$

Solution Steps

Least common multiple of 7 and 5 is 35. Convert \frac{9}{7} and \frac{6}{5} to fractions with denominator 35.

$$\frac{\frac{45}{35}+\frac{42}{35}-\frac{15}{13}}{\frac{5}{12}-\frac{3}{7}-\frac{2}{5}}$$

Since \frac{45}{35} and \frac{42}{35} have the same denominator, add them by adding their numerators.

$$\frac{\frac{45+42}{35}-\frac{15}{13}}{\frac{5}{12}-\frac{3}{7}-\frac{2}{5}}$$

Add 45 and 42 to get 87.

$$\frac{\frac{87}{35}-\frac{15}{13}}{\frac{5}{12}-\frac{3}{7}-\frac{2}{5}}$$

Least common multiple of 35 and 13 is 455. Convert \frac{87}{35} and \frac{15}{13} to fractions with denominator 455.

$$\frac{\frac{1131}{455}-\frac{525}{455}}{\frac{5}{12}-\frac{3}{7}-\frac{2}{5}}$$

Since \frac{1131}{455} and \frac{525}{455} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1131-525}{455}}{\frac{5}{12}-\frac{3}{7}-\frac{2}{5}}$$

Subtract 525 from 1131 to get 606.

$$\frac{\frac{606}{455}}{\frac{5}{12}-\frac{3}{7}-\frac{2}{5}}$$

Least common multiple of 12 and 7 is 84. Convert \frac{5}{12} and \frac{3}{7} to fractions with denominator 84.

$$\frac{\frac{606}{455}}{\frac{35}{84}-\frac{36}{84}-\frac{2}{5}}$$

Since \frac{35}{84} and \frac{36}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{606}{455}}{\frac{35-36}{84}-\frac{2}{5}}$$

Subtract 36 from 35 to get -1.

$$\frac{\frac{606}{455}}{-\frac{1}{84}-\frac{2}{5}}$$

Least common multiple of 84 and 5 is 420. Convert -\frac{1}{84} and \frac{2}{5} to fractions with denominator 420.

$$\frac{\frac{606}{455}}{-\frac{5}{420}-\frac{168}{420}}$$

Since -\frac{5}{420} and \frac{168}{420} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{606}{455}}{\frac{-5-168}{420}}$$

Subtract 168 from -5 to get -173.

$$\frac{\frac{606}{455}}{-\frac{173}{420}}$$

Divide \frac{606}{455} by -\frac{173}{420} by multiplying \frac{606}{455} by the reciprocal of -\frac{173}{420}.

$$\frac{606}{455}\left(-\frac{420}{173}\right)$$

Multiply \frac{606}{455} times -\frac{420}{173} by multiplying numerator times numerator and denominator times denominator.

$$\frac{606\left(-420\right)}{455\times 173}$$

Do the multiplications in the fraction \frac{606\left(-420\right)}{455\times 173}.

$$\frac{-254520}{78715}$$

Reduce the fraction \frac{-254520}{78715} to lowest terms by extracting and canceling out 35.

$$-\frac{7272}{2249}$$

Factor

$$-\frac{7272}{2249} = -3\frac{525}{2249} = -3.2334370831480657$$