\(\left(3-\frac{1}{4}+\frac{2}{5}\right)-\left(5+\frac{1}{3}-\frac{1}{6}\right)-\left(6-\frac{7}{4}+\frac{3}{2}\right)\)
\(=\left(\frac{60-5+8}{20}\right)-\left(\frac{90+6-3}{18}\right)-\left(\frac{48-14+12}{8}\right)\)
\(=\frac{63}{20}-\frac{93}{18}-\frac{23}{4}\)
\(=\frac{567-930-1035}{180}=-\frac{1398}{180}=-\frac{233}{30}\)