[tex]\frac{cos\ 150^o\ \cdot\ tg\ 120^o}{\sqrt3\ sin\ 120^o-tg\ 135^o}=\\\\=\frac{cos\ (90^o+60^o)\ \cdot\ tg\ (90^o+30^o)}{\sqrt3\ \cdot\ sin(90^o+30^o)-tg\ (90^o+45^o)}=\\\\=\frac{-sin\ 60^o\ \cdot\ (-ctg\ 30^o)}{\sqrt3\ \cdot\ cos\ 30^o-(-ctg\ 45^o)}=\\\\=\frac{sin\ 60^o\ \cdot\ ctg\ 30^o}{\sqrt3\ \cdot\ cos\ 30^o\ +ctg\ 45^o}=\\\\=\frac{\frac{\sqrt3}2\ \cdot\ \sqrt3}{\sqrt3\ \cdot\ \frac{\sqrt3}2+1}=\\\\=\frac{\frac32}{\frac32+1}=[/tex]
[tex]=\frac{\frac32}{1\frac32}=\\\\=\frac{\frac32}{\frac52}=\\\\=\frac32\ :\ \frac52=\\\\=\frac32\ \cdot\ \frac25=\\\\=\frac35[/tex]
