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

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

Verify

Solution Steps

Multiply both sides of the equation by 4, the least common multiple of 2,4.

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

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

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

Subtract 3 from 2 to get -1.

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

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

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

Multiply 2 and -1 to get -2.

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

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

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

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

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

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

$$4\left(\frac{9}{4}-1\sqrt{\frac{1}{8}}\sqrt{\frac{1}{2}}\right)+2\left(1-\frac{3}{5}\right)=5$$

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

$$4\left(\frac{9}{4}-\sqrt{\frac{1}{16}}\right)+2\left(1-\frac{3}{5}\right)=5$$

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.

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

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

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

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

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

Multiply 4 and 2 to get 8.

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

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

$$8+2\times \frac{2}{5}=5$$

Multiply 2 and \frac{2}{5} to get \frac{4}{5}.

$$8+\frac{4}{5}=5$$

Add 8 and \frac{4}{5} to get \frac{44}{5}.

$$\frac{44}{5}=5$$

Convert 5 to fraction \frac{25}{5}.

$$\frac{44}{5}=\frac{25}{5}$$

Compare \frac{44}{5} and \frac{25}{5}.

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