Risolvi la seguente espressione

$$\frac{5}{4}\cdot \left [ \left ( \frac{2}{5}+\frac{1}{2}-\frac{3}{4} \right )\cdot \left ( \frac{3}{4}+2+\frac{7}{12} \right )+\frac{3}{5}\cdot \frac{1}{2} \right ]=$$

m.c.m.(5;2;4)=20 – m.c.m.(4;12)=12

$$\frac{5}{4}\cdot \left [ \left ( \frac{8+10-15}{20}\right )\cdot \left ( \frac{9+24+7}{12} \right )+\frac{3}{10}\right]=$$

$$\frac{5}{4}\cdot \left [ \frac{3}{20}\cdot \frac{40}{12} +\frac{3}{10}\right]=$$

$$\frac{5}{4}\cdot \left [ \frac{3}{\cancelto{1}{20}}\cdot \frac{\cancelto{2}{40}}{12}+\frac{3}{10}\right]$$

$$\frac{5}{4}\cdot \left [ 3\cdot \frac{2}{12} +\frac{3}{10}\right]=$$

$$\frac{5}{4}\cdot \left [ 3\cdot \frac{\cancelto{1}{2}}{\cancelto{6}{12}} +\frac{3}{10}\right]=$$

$$\frac{5}{4}\cdot \left [ \frac{1}{2} +\frac{3}{10}\right]=$$

$$\frac{5}{4}\cdot \left [ \frac{5+3}{10}\right]=$$

$$\frac{5}{4}\cdot \frac{8}{10}=$$

$$\frac{5}{4}\cdot \frac{4}{5}=$$

$$\frac{\cancelto{1}{5}}{\cancelto{1}{4}}\cdot \frac{\cancelto{1}{5}}{\cancelto{1}{4}}=$$

$$1$$