[tex]\frac{\sqrt{7}+\sqrt{5} }{\sqrt{7}-\sqrt{5}} -\sqrt{35} =\frac{(\sqrt{7}+\sqrt{5} )(\sqrt{7}+\sqrt{5} ) }{(\sqrt{7}+\sqrt{5})(\sqrt{7}-\sqrt{5}) } -\sqrt{35}= \frac{(\sqrt{7})^2+2\cdot\sqrt{7} \sqrt{5} +(\sqrt{5} )^2 }{(\sqrt{7})^2-(\sqrt{5})^2 } -\sqrt{35}=\\\\=\frac{7+2\cdot\sqrt{35} +5 }{7-5} -\sqrt{35}=\frac{12+2\cdot\sqrt{35} }{2} -\sqrt{35}=\frac{2(6+\sqrt{35} ) }{2} -\sqrt{35}=6-\sqrt{35}-\sqrt{35}=6[/tex]