Lutasin ang [-1+3/2-(-3/4-(-1-1/6))]sqrt{2-frac{7/4}}{(-frac{5}{3})^-1+frac{1}{2}-(-2)^-2}

$$\frac { [ - 1 + \frac { 3 } { 2 } - ( - \frac { 3 } { 4 } - ( - 1 - \frac { 1 } { 6 } ) ) ] \sqrt { 2 - \frac { 7 } { 4 } } } { ( - \frac { 5 } { 3 } ) ^ { - 1 } + \frac { 1 } { 2 } - ( - 2 ) ^ { - 2 } }$$

I-evaluate

$$-\frac{5}{42}\approx -0.119047619$$

Mga Hakbang ng Solution

Idagdag ang -1 at \frac{3}{2} para makuha ang \frac{1}{2}.

$$\frac{\left(\frac{1}{2}-\left(-\frac{3}{4}-\left(-1-\frac{1}{6}\right)\right)\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

I-subtract ang \frac{1}{6} mula sa -1 para makuha ang -\frac{7}{6}.

$$\frac{\left(\frac{1}{2}-\left(-\frac{3}{4}-\left(-\frac{7}{6}\right)\right)\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Ang kabaliktaran ng -\frac{7}{6} ay \frac{7}{6}.

$$\frac{\left(\frac{1}{2}-\left(-\frac{3}{4}+\frac{7}{6}\right)\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Idagdag ang -\frac{3}{4} at \frac{7}{6} para makuha ang \frac{5}{12}.

$$\frac{\left(\frac{1}{2}-\frac{5}{12}\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

I-subtract ang \frac{5}{12} mula sa \frac{1}{2} para makuha ang \frac{1}{12}.

$$\frac{\frac{1}{12}\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

I-subtract ang \frac{7}{4} mula sa 2 para makuha ang \frac{1}{4}.

$$\frac{\frac{1}{12}\sqrt{\frac{1}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

I-rewrite ang square root ng division na \frac{1}{4} bilang division ng mga square root na \frac{\sqrt{1}}{\sqrt{4}}. Kunin ang square root ng numerator at denominator.

$$\frac{\frac{1}{12}\times \frac{1}{2}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

I-multiply ang \frac{1}{12} at \frac{1}{2} para makuha ang \frac{1}{24}.

$$\frac{\frac{1}{24}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Kalkulahin ang -\frac{5}{3} sa power ng -1 at kunin ang -\frac{3}{5}.

$$\frac{\frac{1}{24}}{-\frac{3}{5}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Idagdag ang -\frac{3}{5} at \frac{1}{2} para makuha ang -\frac{1}{10}.

$$\frac{\frac{1}{24}}{-\frac{1}{10}-\left(-2\right)^{-2}}$$

Kalkulahin ang -2 sa power ng -2 at kunin ang \frac{1}{4}.

$$\frac{\frac{1}{24}}{-\frac{1}{10}-\frac{1}{4}}$$

I-subtract ang \frac{1}{4} mula sa -\frac{1}{10} para makuha ang -\frac{7}{20}.

$$\frac{\frac{1}{24}}{-\frac{7}{20}}$$

I-divide ang \frac{1}{24} gamit ang -\frac{7}{20} sa pamamagitan ng pagmu-multiply sa \frac{1}{24} gamit ang reciprocal ng -\frac{7}{20}.

$$\frac{1}{24}\left(-\frac{20}{7}\right)$$

I-multiply ang \frac{1}{24} at -\frac{20}{7} para makuha ang -\frac{5}{42}.

$$-\frac{5}{42}$$

I-factor

$$-\frac{5}{42} = -0.11904761904761904$$