Solve -6/5-2(9/2+5/15)*(frac{3/4+(frac{9}{7}-frac{3}{4}))}{-(frac{3}{20}-frac{3}{30})div(frac{4}{3}(frac{9}{8}+frac{8}{9}))-(frac{3}{4}-frac{9}{12})}

$$\frac { - \frac { 6 } { 5 } - 2 ( \frac { 9 } { 2 } + \frac { 5 } { 15 } ) \cdot ( \frac { 3 } { 4 } + ( \frac { 9 } { 7 } - \frac { 3 } { 4 } ) ) } { - ( \frac { 3 } { 20 } - \frac { 3 } { 30 } ) \div ( \frac { 4 } { 3 } ( \frac { 9 } { 8 } + \frac { 8 } { 9 } ) ) - ( \frac { 3 } { 4 } - \frac { 9 } { 12 } ) }$$

Evaluate

$$\frac{15370}{21}\approx 731.904761905$$

Solution Steps

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{6}{5}-2\left(\frac{9}{2}+\frac{1}{3}\right)\left(\frac{3}{4}+\frac{9}{7}-\frac{3}{4}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Least common multiple of 2 and 3 is 6. Convert \frac{9}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{-\frac{6}{5}-2\left(\frac{27}{6}+\frac{2}{6}\right)\left(\frac{3}{4}+\frac{9}{7}-\frac{3}{4}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Since \frac{27}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{6}{5}-2\times \frac{27+2}{6}\left(\frac{3}{4}+\frac{9}{7}-\frac{3}{4}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Add 27 and 2 to get 29.

$$\frac{-\frac{6}{5}-2\times \frac{29}{6}\left(\frac{3}{4}+\frac{9}{7}-\frac{3}{4}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Express 2\times \frac{29}{6} as a single fraction.

$$\frac{-\frac{6}{5}-\frac{2\times 29}{6}\left(\frac{3}{4}+\frac{9}{7}-\frac{3}{4}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Multiply 2 and 29 to get 58.

$$\frac{-\frac{6}{5}-\frac{58}{6}\left(\frac{3}{4}+\frac{9}{7}-\frac{3}{4}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Reduce the fraction \frac{58}{6} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{6}{5}-\frac{29}{3}\left(\frac{3}{4}+\frac{9}{7}-\frac{3}{4}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Least common multiple of 4 and 7 is 28. Convert \frac{3}{4} and \frac{9}{7} to fractions with denominator 28.

$$\frac{-\frac{6}{5}-\frac{29}{3}\left(\frac{21}{28}+\frac{36}{28}-\frac{3}{4}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Since \frac{21}{28} and \frac{36}{28} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{6}{5}-\frac{29}{3}\left(\frac{21+36}{28}-\frac{3}{4}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Add 21 and 36 to get 57.

$$\frac{-\frac{6}{5}-\frac{29}{3}\left(\frac{57}{28}-\frac{3}{4}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Least common multiple of 28 and 4 is 28. Convert \frac{57}{28} and \frac{3}{4} to fractions with denominator 28.

$$\frac{-\frac{6}{5}-\frac{29}{3}\left(\frac{57}{28}-\frac{21}{28}\right)}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Since \frac{57}{28} and \frac{21}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{6}{5}-\frac{29}{3}\times \frac{57-21}{28}}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Subtract 21 from 57 to get 36.

$$\frac{-\frac{6}{5}-\frac{29}{3}\times \frac{36}{28}}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Reduce the fraction \frac{36}{28} to lowest terms by extracting and canceling out 4.

$$\frac{-\frac{6}{5}-\frac{29}{3}\times \frac{9}{7}}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Multiply \frac{29}{3} times \frac{9}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{6}{5}-\frac{29\times 9}{3\times 7}}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Do the multiplications in the fraction \frac{29\times 9}{3\times 7}.

$$\frac{-\frac{6}{5}-\frac{261}{21}}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Reduce the fraction \frac{261}{21} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{6}{5}-\frac{87}{7}}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Least common multiple of 5 and 7 is 35. Convert -\frac{6}{5} and \frac{87}{7} to fractions with denominator 35.

$$\frac{-\frac{42}{35}-\frac{435}{35}}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Since -\frac{42}{35} and \frac{435}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-42-435}{35}}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Subtract 435 from -42 to get -477.

$$\frac{-\frac{477}{35}}{\frac{-\left(\frac{3}{20}-\frac{3}{30}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Reduce the fraction \frac{3}{30} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{477}{35}}{\frac{-\left(\frac{3}{20}-\frac{1}{10}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Least common multiple of 20 and 10 is 20. Convert \frac{3}{20} and \frac{1}{10} to fractions with denominator 20.

$$\frac{-\frac{477}{35}}{\frac{-\left(\frac{3}{20}-\frac{2}{20}\right)}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Since \frac{3}{20} and \frac{2}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{477}{35}}{\frac{-\frac{3-2}{20}}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Subtract 2 from 3 to get 1.

$$\frac{-\frac{477}{35}}{\frac{-\frac{1}{20}}{\frac{4}{3}\left(\frac{9}{8}+\frac{8}{9}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Least common multiple of 8 and 9 is 72. Convert \frac{9}{8} and \frac{8}{9} to fractions with denominator 72.

$$\frac{-\frac{477}{35}}{\frac{-\frac{1}{20}}{\frac{4}{3}\left(\frac{81}{72}+\frac{64}{72}\right)}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Since \frac{81}{72} and \frac{64}{72} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{477}{35}}{\frac{-\frac{1}{20}}{\frac{4}{3}\times \frac{81+64}{72}}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Add 81 and 64 to get 145.

$$\frac{-\frac{477}{35}}{\frac{-\frac{1}{20}}{\frac{4}{3}\times \frac{145}{72}}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Multiply \frac{4}{3} times \frac{145}{72} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{477}{35}}{\frac{-\frac{1}{20}}{\frac{4\times 145}{3\times 72}}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Do the multiplications in the fraction \frac{4\times 145}{3\times 72}.

$$\frac{-\frac{477}{35}}{\frac{-\frac{1}{20}}{\frac{580}{216}}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Reduce the fraction \frac{580}{216} to lowest terms by extracting and canceling out 4.

$$\frac{-\frac{477}{35}}{\frac{-\frac{1}{20}}{\frac{145}{54}}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Divide -\frac{1}{20} by \frac{145}{54} by multiplying -\frac{1}{20} by the reciprocal of \frac{145}{54}.

$$\frac{-\frac{477}{35}}{-\frac{1}{20}\times \frac{54}{145}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Multiply -\frac{1}{20} times \frac{54}{145} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\frac{477}{35}}{\frac{-54}{20\times 145}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Do the multiplications in the fraction \frac{-54}{20\times 145}.

$$\frac{-\frac{477}{35}}{\frac{-54}{2900}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Reduce the fraction \frac{-54}{2900} to lowest terms by extracting and canceling out 2.

$$\frac{-\frac{477}{35}}{-\frac{27}{1450}-\left(\frac{3}{4}-\frac{9}{12}\right)}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{477}{35}}{-\frac{27}{1450}-\left(\frac{3}{4}-\frac{3}{4}\right)}$$

Subtract \frac{3}{4} from \frac{3}{4} to get 0.

$$\frac{-\frac{477}{35}}{-\frac{27}{1450}-0}$$

Subtract 0 from -\frac{27}{1450} to get -\frac{27}{1450}.

$$\frac{-\frac{477}{35}}{-\frac{27}{1450}}$$

Divide -\frac{477}{35} by -\frac{27}{1450} by multiplying -\frac{477}{35} by the reciprocal of -\frac{27}{1450}.

$$-\frac{477}{35}\left(-\frac{1450}{27}\right)$$

Multiply -\frac{477}{35} times -\frac{1450}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-477\left(-1450\right)}{35\times 27}$$

Do the multiplications in the fraction \frac{-477\left(-1450\right)}{35\times 27}.

$$\frac{691650}{945}$$

Reduce the fraction \frac{691650}{945} to lowest terms by extracting and canceling out 45.

$$\frac{15370}{21}$$

Factor

$$\frac{2 \cdot 5 \cdot 29 \cdot 53}{3 \cdot 7} = 731\frac{19}{21} = 731.9047619047619$$