Solve {left(2/frac{3{2-3}}-2right)}^2-sqrt{1/8}*sqrt{1/2}+1-frac{3/5}{2}

$${ \left( \frac{ 2 }{ \frac{ 3 }{ 2-3 } } -2 \right) }^{ 2 } - \sqrt{ \frac{ 1 }{ 8 } } \times \sqrt{ \frac{ 1 }{ 2 } } + \frac{ 1- \frac{ 3 }{ 5 } }{ 2 }$$

Evaluate

$$\frac{1271}{180}\approx 7.061111111$$

Solution Steps

Divide 2 by \frac{3}{2-3} by multiplying 2 by the reciprocal of \frac{3}{2-3}.

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

Subtract 3 from 2 to get -1.

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

Multiply 2 and -1 to get -2.

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

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

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

Subtract 2 from -\frac{2}{3} to get -\frac{8}{3}.

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

Calculate -\frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$\frac{64}{9}-\sqrt{\frac{1}{8}}\sqrt{\frac{1}{2}}+\frac{1-\frac{3}{5}}{2}$$

To multiply \sqrt{\frac{1}{8}} and \sqrt{\frac{1}{2}}, multiply the numbers under the square root.

$$\frac{64}{9}-\sqrt{\frac{1}{16}}+\frac{1-\frac{3}{5}}{2}$$

Rewrite the square root of the division \frac{1}{16} as the division of square roots \frac{\sqrt{1}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{64}{9}-\frac{1}{4}+\frac{1-\frac{3}{5}}{2}$$

Subtract \frac{1}{4} from \frac{64}{9} to get \frac{247}{36}.

$$\frac{247}{36}+\frac{1-\frac{3}{5}}{2}$$

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

$$\frac{247}{36}+\frac{\frac{2}{5}}{2}$$

Express \frac{\frac{2}{5}}{2} as a single fraction.

$$\frac{247}{36}+\frac{2}{5\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{247}{36}+\frac{1}{5}$$

Add \frac{247}{36} and \frac{1}{5} to get \frac{1271}{180}.

$$\frac{1271}{180}$$

Factor

$$\frac{31 \cdot 41}{2 ^ {2} \cdot 3 ^ {2} \cdot 5} = 7\frac{11}{180} = 7.061111111111111$$