[tex]1)\frac{a+6}{a^{2} -36}=\frac{a+6}{(a+6)(a-6)}=\boxed{\frac{1}{a-6}}\\\\2)\frac{3x+27y}{9xy} =\frac{3(x+9y)}{9xy}=\boxed{\frac{x+9y}{3xy}}\\\\3)\frac{y^{2} }{y^{2}+5y }=\frac{y^{2} }{y(y+5)}=\boxed{\frac{y}{y+5}} \\\\4)\frac{a^{2}-10a+25 }{a-5}=\frac{(a-5)^{2} }{a-5}=\boxed{a-5}\\\\5)\frac{y^{2} +8y+16}{y^{2}-16 }=\frac{(y+4)^{2} }{(y+4)(y-4)}=\boxed{\frac{y+4}{y-4}}\\\\6)\frac{xy-49y^{2} }{x^{2} -49xy} =\frac{y(x-49y)}{x(x-49y)} =\boxed{\frac{y}{x}}[/tex]
