Solve (3/2)^-1{2/3-[(1-frac{1/3)-(-3)^-1]}-(1/2+frac{3}{4})}{(1-frac{1}{3}){-1-[-frac{2}{3}+(1+frac{1}{3})*3^-1]}+1}

$$\frac { ( \frac { 3 } { 2 } ) ^ { - 1 } \{ \frac { 2 } { 3 } - [ ( 1 - \frac { 1 } { 3 } ) - ( - 3 ) ^ { - 1 } ] \} - ( \frac { 1 } { 2 } + \frac { 3 } { 4 } ) } { ( 1 - \frac { 1 } { 3 } ) \{ - 1 - [ - \frac { 2 } { 3 } + ( 1 + \frac { 1 } { 3 } ) \cdot 3 ^ { - 1 } ] \} + 1 }$$

Evaluate

$$-\frac{159}{52}\approx -3.057692308$$

Solution Steps

Calculate \frac{3}{2} to the power of -1 and get \frac{2}{3}.

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

Subtract \frac{1}{3} from 1 to get \frac{2}{3}.

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

Calculate -3 to the power of -1 and get -\frac{1}{3}.

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

The opposite of -\frac{1}{3} is \frac{1}{3}.

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

Add \frac{2}{3} and \frac{1}{3} to get 1.

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

Subtract 1 from \frac{2}{3} to get -\frac{1}{3}.

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

Multiply \frac{2}{3} and -\frac{1}{3} to get -\frac{2}{9}.

$$\frac{-\frac{2}{9}-\left(\frac{1}{2}+\frac{3}{4}\right)}{\left(1-\frac{1}{3}\right)\left(-1-\left(-\frac{2}{3}+\left(1+\frac{1}{3}\right)\times 3^{-1}\right)\right)+1}$$

Add \frac{1}{2} and \frac{3}{4} to get \frac{5}{4}.

$$\frac{-\frac{2}{9}-\frac{5}{4}}{\left(1-\frac{1}{3}\right)\left(-1-\left(-\frac{2}{3}+\left(1+\frac{1}{3}\right)\times 3^{-1}\right)\right)+1}$$

Subtract \frac{5}{4} from -\frac{2}{9} to get -\frac{53}{36}.

$$\frac{-\frac{53}{36}}{\left(1-\frac{1}{3}\right)\left(-1-\left(-\frac{2}{3}+\left(1+\frac{1}{3}\right)\times 3^{-1}\right)\right)+1}$$

Subtract \frac{1}{3} from 1 to get \frac{2}{3}.

$$\frac{-\frac{53}{36}}{\frac{2}{3}\left(-1-\left(-\frac{2}{3}+\left(1+\frac{1}{3}\right)\times 3^{-1}\right)\right)+1}$$

Add 1 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{-\frac{53}{36}}{\frac{2}{3}\left(-1-\left(-\frac{2}{3}+\frac{4}{3}\times 3^{-1}\right)\right)+1}$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{-\frac{53}{36}}{\frac{2}{3}\left(-1-\left(-\frac{2}{3}+\frac{4}{3}\times \frac{1}{3}\right)\right)+1}$$

Multiply \frac{4}{3} and \frac{1}{3} to get \frac{4}{9}.

$$\frac{-\frac{53}{36}}{\frac{2}{3}\left(-1-\left(-\frac{2}{3}+\frac{4}{9}\right)\right)+1}$$

Add -\frac{2}{3} and \frac{4}{9} to get -\frac{2}{9}.

$$\frac{-\frac{53}{36}}{\frac{2}{3}\left(-1-\left(-\frac{2}{9}\right)\right)+1}$$

The opposite of -\frac{2}{9} is \frac{2}{9}.

$$\frac{-\frac{53}{36}}{\frac{2}{3}\left(-1+\frac{2}{9}\right)+1}$$

Add -1 and \frac{2}{9} to get -\frac{7}{9}.

$$\frac{-\frac{53}{36}}{\frac{2}{3}\left(-\frac{7}{9}\right)+1}$$

Multiply \frac{2}{3} and -\frac{7}{9} to get -\frac{14}{27}.

$$\frac{-\frac{53}{36}}{-\frac{14}{27}+1}$$

Add -\frac{14}{27} and 1 to get \frac{13}{27}.

$$\frac{-\frac{53}{36}}{\frac{13}{27}}$$

Divide -\frac{53}{36} by \frac{13}{27} by multiplying -\frac{53}{36} by the reciprocal of \frac{13}{27}.

$$-\frac{53}{36}\times \frac{27}{13}$$

Multiply -\frac{53}{36} and \frac{27}{13} to get -\frac{159}{52}.

$$-\frac{159}{52}$$

Factor

$$-\frac{159}{52} = -3\frac{3}{52} = -3.0576923076923075$$