Solve {2/3+[(5/3+8/3)div(2/3-frac{9}{5})]}

$$\{ \frac { 2 } { 3 } + [ ( \frac { 5 } { 3 } + \frac { 8 } { 3 } ) \div ( \frac { 2 } { 3 } - \frac { 9 } { 5 } ) ] \}$$

Evaluate

$$-\frac{161}{51}\approx -3.156862745$$

Solution Steps

Since \frac{5}{3} and \frac{8}{3} have the same denominator, add them by adding their numerators.

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

Add 5 and 8 to get 13.

$$\frac{2}{3}+\frac{\frac{13}{3}}{\frac{2}{3}-\frac{9}{5}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{9}{5} to fractions with denominator 15.

$$\frac{2}{3}+\frac{\frac{13}{3}}{\frac{10}{15}-\frac{27}{15}}$$

Since \frac{10}{15} and \frac{27}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{3}+\frac{\frac{13}{3}}{\frac{10-27}{15}}$$

Subtract 27 from 10 to get -17.

$$\frac{2}{3}+\frac{\frac{13}{3}}{-\frac{17}{15}}$$

Divide \frac{13}{3} by -\frac{17}{15} by multiplying \frac{13}{3} by the reciprocal of -\frac{17}{15}.

$$\frac{2}{3}+\frac{13}{3}\left(-\frac{15}{17}\right)$$

Multiply \frac{13}{3} times -\frac{15}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{3}+\frac{13\left(-15\right)}{3\times 17}$$

Do the multiplications in the fraction \frac{13\left(-15\right)}{3\times 17}.

$$\frac{2}{3}+\frac{-195}{51}$$

Reduce the fraction \frac{-195}{51} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}-\frac{65}{17}$$

Least common multiple of 3 and 17 is 51. Convert \frac{2}{3} and \frac{65}{17} to fractions with denominator 51.

$$\frac{34}{51}-\frac{195}{51}$$

Since \frac{34}{51} and \frac{195}{51} have the same denominator, subtract them by subtracting their numerators.

$$\frac{34-195}{51}$$

Subtract 195 from 34 to get -161.

$$-\frac{161}{51}$$

Factor

$$-\frac{161}{51} = -3\frac{8}{51} = -3.156862745098039$$