[tex]\dfrac{sin^{2}60^{o}-tg^{2}60^{o}}{sin30^{o}+tg45^{o}}=\dfrac{(\dfrac{\sqrt{3}}{2})^{2}-\sqrt{3}^{2}}{\dfrac{1}{2}+1} = \dfrac{\dfrac{3}{4}-3}{\dfrac{3}{2}} = \dfrac{\frac{3}{4}-\dfrac{12}{4}}{\dfrac{3}{2}}=-\dfrac{9}{4}\cdot\dfrac{2}{3}}=-\dfrac{3}{2}=-1\dfrac{1}{2}[/tex]
