Risolvi la seguente espressione

$$\left[ \left( 1-\dfrac{3}{4}+\dfrac{1}{5}\right) \left( \dfrac{1}{2}+\dfrac{1}{3}\right) -\left( \dfrac{3}{5}-\dfrac{1}{2}+\dfrac{1}{6}\right) :\dfrac{16}{15}\right] \cdot \dfrac{4}{3}+1=$$

$$\left[ \left( \dfrac{20-15+4}{20}\right) \left( \dfrac{3+2}{6}\right) -\left( \dfrac{18-15+5}{30}\right) \cdot \dfrac{15}{16}\right] \cdot \dfrac{4}{3}+1=$$

$$\left[ \dfrac{9}{20}\cdot \dfrac{5}{6}-\dfrac{8}{30}\cdot \dfrac{15}{16}\right] \cdot \dfrac{4}{3}+1=$$

$$\left[ \dfrac{3}{8}-\dfrac{1}{4}\right] \cdot \dfrac{4}{3}+1=$$

$$\left[\dfrac{3-2}{8}\right] \cdot \dfrac{4}{3}+1=$$

$$\dfrac{1}{8}\cdot \dfrac{4}{3}+1=$$

$$\dfrac{1}{6}+1=$$

$$\dfrac{1+6}{6}=$$

$$\dfrac{7}{6}$$