Solve {left(3/2-1/2-3-1right)}^2-sqrt{1/8}sqrt{1/2}+frac{1-frac{3}{5}}{2}-frac{5}{4}

$${ \left( \frac{ \frac{ 3 }{ 2 } -1 }{ 2-3 } -1 \right) }^{ 2 } - \sqrt{ \frac{ 1 }{ 8 } } \sqrt{ \frac{ 1 }{ 2 } } + \frac{ 1- \frac{ 3 }{ 5 } }{ 2 } - \frac{ 5 }{ 4 }$$

Evaluate

$$\frac{19}{20}=0.95$$

Solution Steps

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

$$\left(\frac{\frac{1}{2}}{2-3}-1\right)^{2}-\sqrt{\frac{1}{8}}\sqrt{\frac{1}{2}}+\frac{1-\frac{3}{5}}{2}-\frac{5}{4}$$

Subtract 3 from 2 to get -1.

$$\left(\frac{\frac{1}{2}}{-1}-1\right)^{2}-\sqrt{\frac{1}{8}}\sqrt{\frac{1}{2}}+\frac{1-\frac{3}{5}}{2}-\frac{5}{4}$$

Express \frac{\frac{1}{2}}{-1} as a single fraction.

$$\left(\frac{1}{2\left(-1\right)}-1\right)^{2}-\sqrt{\frac{1}{8}}\sqrt{\frac{1}{2}}+\frac{1-\frac{3}{5}}{2}-\frac{5}{4}$$

Multiply 2 and -1 to get -2.

$$\left(\frac{1}{-2}-1\right)^{2}-\sqrt{\frac{1}{8}}\sqrt{\frac{1}{2}}+\frac{1-\frac{3}{5}}{2}-\frac{5}{4}$$

Fraction \frac{1}{-2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\left(-\frac{1}{2}-1\right)^{2}-\sqrt{\frac{1}{8}}\sqrt{\frac{1}{2}}+\frac{1-\frac{3}{5}}{2}-\frac{5}{4}$$

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

$$\left(-\frac{3}{2}\right)^{2}-\sqrt{\frac{1}{8}}\sqrt{\frac{1}{2}}+\frac{1-\frac{3}{5}}{2}-\frac{5}{4}$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{9}{4}-\sqrt{\frac{1}{8}}\sqrt{\frac{1}{2}}+\frac{1-\frac{3}{5}}{2}-\frac{5}{4}$$

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

$$\frac{9}{4}-\sqrt{\frac{1}{16}}+\frac{1-\frac{3}{5}}{2}-\frac{5}{4}$$

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.

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

Subtract \frac{1}{4} from \frac{9}{4} to get 2.

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

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

$$2+\frac{\frac{2}{5}}{2}-\frac{5}{4}$$

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

$$2+\frac{2}{5\times 2}-\frac{5}{4}$$

Cancel out 2 in both numerator and denominator.

$$2+\frac{1}{5}-\frac{5}{4}$$

Add 2 and \frac{1}{5} to get \frac{11}{5}.

$$\frac{11}{5}-\frac{5}{4}$$

Subtract \frac{5}{4} from \frac{11}{5} to get \frac{19}{20}.

$$\frac{19}{20}$$

Factor

$$\frac{19}{2 ^ {2} \cdot 5} = 0.95$$