[tex]\displaystyle\bf\\1)\\\\\Big(\frac{a}{b} -\frac{b}{a} \Big)\cdot\frac{6ab}{a-b} =\frac{a^{2}-b^{2} }{ab}\cdot\frac{6ab}{a-b} =\frac{(a-b)(a+b)\cdot 6}{a-b}=\boxed{6(a+b) }\\\\\\2)\\\\\frac{1}{t+y} +\frac{3ty}{t^{3} +y^{3} } =\frac{1}{t+y} +\frac{3ty}{(t+y)(t^{2}-ty+y^{2} ) } =\\\\\\=\frac{t^{2}-ty+y^{2} +3ty }{(t+y)(t^{2} -ty+y^{2} )} ==\frac{t^{2}+2ty+y^{2} }{(t+y)(t^{2} -ty+y^{2} )} =\\\\\\==\frac{(t+y)^{2}}{(t+y)(t^{2} -ty+y^{2} )} =\boxed{\frac{t+y}{t^{2}-ty+y^{2} } }[/tex]