Solve (3/4+-2/3)+(1/5-frac{-3/2)}{frac{3}{5}-(frac{2}{3}+frac{1}{2})}=

$$\frac{ ( \frac{ 3 }{ 4 } + \frac{ -2 }{ 3 } )+( \frac{ 1 }{ 5 } - \frac{ -3 }{ 2 } ) }{ \frac{ 3 }{ 5 } -( \frac{ 2 }{ 3 } + \frac{ 1 }{ 2 } ) } =$$

Evaluate

$$-\frac{107}{34}\approx -3.147058824$$

Solution Steps

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\frac{\frac{3}{4}-\frac{2}{3}+\frac{1}{5}-\frac{-3}{2}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{\frac{9}{12}-\frac{8}{12}+\frac{1}{5}-\frac{-3}{2}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-8}{12}+\frac{1}{5}-\frac{-3}{2}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

Subtract 8 from 9 to get 1.

$$\frac{\frac{1}{12}+\frac{1}{5}-\frac{-3}{2}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

Least common multiple of 12 and 5 is 60. Convert \frac{1}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{\frac{5}{60}+\frac{12}{60}-\frac{-3}{2}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

Since \frac{5}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+12}{60}-\frac{-3}{2}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

Add 5 and 12 to get 17.

$$\frac{\frac{17}{60}-\frac{-3}{2}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$\frac{\frac{17}{60}-\left(-\frac{3}{2}\right)}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$\frac{\frac{17}{60}+\frac{3}{2}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

Least common multiple of 60 and 2 is 60. Convert \frac{17}{60} and \frac{3}{2} to fractions with denominator 60.

$$\frac{\frac{17}{60}+\frac{90}{60}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

Since \frac{17}{60} and \frac{90}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{17+90}{60}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

Add 17 and 90 to get 107.

$$\frac{\frac{107}{60}}{\frac{3}{5}-\left(\frac{2}{3}+\frac{1}{2}\right)}$$

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

$$\frac{\frac{107}{60}}{\frac{3}{5}-\left(\frac{4}{6}+\frac{3}{6}\right)}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{107}{60}}{\frac{3}{5}-\frac{4+3}{6}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{107}{60}}{\frac{3}{5}-\frac{7}{6}}$$

Least common multiple of 5 and 6 is 30. Convert \frac{3}{5} and \frac{7}{6} to fractions with denominator 30.

$$\frac{\frac{107}{60}}{\frac{18}{30}-\frac{35}{30}}$$

Since \frac{18}{30} and \frac{35}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{107}{60}}{\frac{18-35}{30}}$$

Subtract 35 from 18 to get -17.

$$\frac{\frac{107}{60}}{-\frac{17}{30}}$$

Divide \frac{107}{60} by -\frac{17}{30} by multiplying \frac{107}{60} by the reciprocal of -\frac{17}{30}.

$$\frac{107}{60}\left(-\frac{30}{17}\right)$$

Multiply \frac{107}{60} times -\frac{30}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{107\left(-30\right)}{60\times 17}$$

Do the multiplications in the fraction \frac{107\left(-30\right)}{60\times 17}.

$$\frac{-3210}{1020}$$

Reduce the fraction \frac{-3210}{1020} to lowest terms by extracting and canceling out 30.

$$-\frac{107}{34}$$

Factor

$$-\frac{107}{34} = -3\frac{5}{34} = -3.1470588235294117$$