Solve [(1+1/2)*(3/2)^-1-(2-1/3)*(-5/3)^-2*(+3)^-1]^-1=

$$[ ( 1 + 1 / 2 ) \cdot ( 3 / 2 ) ^ { - 1 } - ( 2 - 1 / 3 ) \cdot ( - 5 / 3 ) ^ { - 2 } \cdot ( + 3 ) ^ { - 1 } ] ^ { - 1 } =$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

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

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

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

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

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

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

Subtract \frac{1}{3} from 2 to get \frac{5}{3}.

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

Calculate -\frac{5}{3} to the power of -2 and get \frac{9}{25}.

$$\left(1-\frac{5}{3}\times \frac{9}{25}\times 3^{-1}\right)^{-1}$$

Multiply \frac{5}{3} and \frac{9}{25} to get \frac{3}{5}.

$$\left(1-\frac{3}{5}\times 3^{-1}\right)^{-1}$$

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

$$\left(1-\frac{3}{5}\times \frac{1}{3}\right)^{-1}$$

Multiply \frac{3}{5} and \frac{1}{3} to get \frac{1}{5}.

$$\left(1-\frac{1}{5}\right)^{-1}$$

Subtract \frac{1}{5} from 1 to get \frac{4}{5}.

$$\left(\frac{4}{5}\right)^{-1}$$

Calculate \frac{4}{5} to the power of -1 and get \frac{5}{4}.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$