Solve 3/5div{[(7/3+1/2)+(2/3-frac{1}{4})^2]*(frac{1}{3}-frac{12}{5})}

$$\frac { 3 } { 5 } \div \{ [ ( \frac { 7 } { 3 } + \frac { 1 } { 2 } ) + ( \frac { 2 } { 3 } - \frac { 1 } { 4 } ) ^ { 2 } ] * ( \frac { 1 } { 3 } - \frac { 12 } { 5 } ) \}$$

Evaluate

$$-\frac{1296}{13423}\approx -0.096550697$$

Solution Steps

Add \frac{7}{3} and \frac{1}{2} to get \frac{17}{6}.

$$\frac{\frac{3}{5}}{\left(\frac{17}{6}+\left(\frac{2}{3}-\frac{1}{4}\right)^{2}\right)\left(\frac{1}{3}-\frac{12}{5}\right)}$$

Subtract \frac{1}{4} from \frac{2}{3} to get \frac{5}{12}.

$$\frac{\frac{3}{5}}{\left(\frac{17}{6}+\left(\frac{5}{12}\right)^{2}\right)\left(\frac{1}{3}-\frac{12}{5}\right)}$$

Calculate \frac{5}{12} to the power of 2 and get \frac{25}{144}.

$$\frac{\frac{3}{5}}{\left(\frac{17}{6}+\frac{25}{144}\right)\left(\frac{1}{3}-\frac{12}{5}\right)}$$

Add \frac{17}{6} and \frac{25}{144} to get \frac{433}{144}.

$$\frac{\frac{3}{5}}{\frac{433}{144}\left(\frac{1}{3}-\frac{12}{5}\right)}$$

Subtract \frac{12}{5} from \frac{1}{3} to get -\frac{31}{15}.

$$\frac{\frac{3}{5}}{\frac{433}{144}\left(-\frac{31}{15}\right)}$$

Multiply \frac{433}{144} and -\frac{31}{15} to get -\frac{13423}{2160}.

$$\frac{\frac{3}{5}}{-\frac{13423}{2160}}$$

Divide \frac{3}{5} by -\frac{13423}{2160} by multiplying \frac{3}{5} by the reciprocal of -\frac{13423}{2160}.

$$\frac{3}{5}\left(-\frac{2160}{13423}\right)$$

Multiply \frac{3}{5} and -\frac{2160}{13423} to get -\frac{1296}{13423}.

$$-\frac{1296}{13423}$$

Factor

$$-\frac{1296}{13423} = -0.09655069656559637$$