Solve sqrt{(frac{-3/4)*(-12)-(-7)}+sqrt[3]{-125/8}}{1/3*(-1/2)+frac{5}{6}*(-1)^-5-(1-frac{1}{4}):(-2)^-1}=3

$$\frac { \sqrt { ( \frac { - 3 } { 4 } ) \cdot ( - 12 ) - ( - 7 ) } + \sqrt[ 3 ] { \frac { - 125 } { 8 } } } { \frac { 1 } { 3 } \cdot ( \frac { - 1 } { 2 } ) + \frac { 5 } { 6 } \cdot ( - 1 ) ^ { - 5 } - ( 1 - \frac { 1 } { 4 } ) : ( - 2 ) ^ { - 1 } } = 3$$

Verify

Solution Steps

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{\sqrt{-\frac{3}{4}\left(-12\right)-\left(-7\right)}+\sqrt[3]{\frac{-125}{8}}}{\frac{1}{3}\times \frac{-1}{2}+\frac{5}{6}\left(-1\right)^{-5}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

Multiply -\frac{3}{4} and -12 to get 9.

$$\frac{\sqrt{9-\left(-7\right)}+\sqrt[3]{\frac{-125}{8}}}{\frac{1}{3}\times \frac{-1}{2}+\frac{5}{6}\left(-1\right)^{-5}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

The opposite of -7 is 7.

$$\frac{\sqrt{9+7}+\sqrt[3]{\frac{-125}{8}}}{\frac{1}{3}\times \frac{-1}{2}+\frac{5}{6}\left(-1\right)^{-5}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

Add 9 and 7 to get 16.

$$\frac{\sqrt{16}+\sqrt[3]{\frac{-125}{8}}}{\frac{1}{3}\times \frac{-1}{2}+\frac{5}{6}\left(-1\right)^{-5}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

Calculate the square root of 16 and get 4.

$$\frac{4+\sqrt[3]{\frac{-125}{8}}}{\frac{1}{3}\times \frac{-1}{2}+\frac{5}{6}\left(-1\right)^{-5}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

Fraction \frac{-125}{8} can be rewritten as -\frac{125}{8} by extracting the negative sign.

$$\frac{4+\sqrt[3]{-\frac{125}{8}}}{\frac{1}{3}\times \frac{-1}{2}+\frac{5}{6}\left(-1\right)^{-5}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

Calculate \sqrt[3]{-\frac{125}{8}} and get -\frac{5}{2}.

$$\frac{4-\frac{5}{2}}{\frac{1}{3}\times \frac{-1}{2}+\frac{5}{6}\left(-1\right)^{-5}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

Subtract \frac{5}{2} from 4 to get \frac{3}{2}.

$$\frac{\frac{3}{2}}{\frac{1}{3}\times \frac{-1}{2}+\frac{5}{6}\left(-1\right)^{-5}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

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

$$\frac{\frac{3}{2}}{\frac{1}{3}\left(-\frac{1}{2}\right)+\frac{5}{6}\left(-1\right)^{-5}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

Multiply \frac{1}{3} and -\frac{1}{2} to get -\frac{1}{6}.

$$\frac{\frac{3}{2}}{-\frac{1}{6}+\frac{5}{6}\left(-1\right)^{-5}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

Calculate -1 to the power of -5 and get -1.

$$\frac{\frac{3}{2}}{-\frac{1}{6}+\frac{5}{6}\left(-1\right)-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

Multiply \frac{5}{6} and -1 to get -\frac{5}{6}.

$$\frac{\frac{3}{2}}{-\frac{1}{6}-\frac{5}{6}-\frac{1-\frac{1}{4}}{\left(-2\right)^{-1}}}=3$$

Subtract \frac{5}{6} from -\frac{1}{6} to get -1.

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

Subtract \frac{1}{4} from 1 to get \frac{3}{4}.

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

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

$$\frac{\frac{3}{2}}{-1-\frac{\frac{3}{4}}{-\frac{1}{2}}}=3$$

Divide \frac{3}{4} by -\frac{1}{2} by multiplying \frac{3}{4} by the reciprocal of -\frac{1}{2}.

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

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

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

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$\frac{\frac{3}{2}}{-1+\frac{3}{2}}=3$$

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

$$\frac{\frac{3}{2}}{\frac{1}{2}}=3$$

Divide \frac{3}{2} by \frac{1}{2} by multiplying \frac{3}{2} by the reciprocal of \frac{1}{2}.

$$\frac{3}{2}\times 2=3$$

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

$$3=3$$

Compare 3 and 3.

$$\text{true}$$

Verify (complex solution)