[tex]\frac{cos150*tg120}{\sqrt3sin120-tg135}=\frac{-cos30*(-ctg30)}{\sqrt3cos30-(-ctg45)}=\frac{-cos30*(-\frac{cos30}{sin30})}{\sqrt3cos30+ctg45}=\frac{\frac{cos^230}{sin30}}{\sqrt3cos30+ctg45}=\\((\frac{\sqrt3}2)^2:\frac12):(\sqrt3*\frac{\sqrt3}2+1)=\\\\(\frac{3}4*2):(\frac{3}2+\frac22)=\frac32:\frac52=\frac32*\frac25=\frac35[/tex]
