Math Problem Solver

\[ -\left( \frac{128}{21} \right) - \frac{32}{5} + \frac{32}{3} + \frac{128}{3} = \frac{4288}{105} = 40.8\overline{380952} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{-128}{21}\), \(\frac{-32}{5}\), \(\frac{32}{3}\), and \(\frac{128}{3}\) is \(105\). \[ \begin{aligned} -\left( \frac{128}{21} \right) - \frac{32}{5} + \frac{32}{3} + \frac{128}{3} &= \frac{-128 \cdot 5}{21 \cdot 5} + \frac{-32 \cdot 21}{5 \cdot 21} + \frac{32 \cdot 35}{3 \cdot 35} + \frac{128 \cdot 35}{3 \cdot 35} \\ &= \frac{-640 + -672 + 1120 + 4480}{105} \\ &= \frac{4288}{105} \end{aligned} \]