[tex]\displaystyle\bf\\\frac{a^{2}+16 }{a^{2} -16} +\frac{4}{a+4}+\frac{4}{a-4} =\frac{a^{2}+16 }{(a+4)(a-4)} +\frac{4}{a+4}+\frac{4}{a-4} = \\\\\\=\frac{a^{2} +16+4\cdot(a-4)+4\cdot(a+4)}{(a+4)(a-4)} =\\\\\\=\frac{a^{2} +16+4a-16+4a+16}{(a+4)(a-4)} =\frac{a^{2} +8a+16}{(a+4)(a-4)} =\\\\\\=\frac{(a+4)^{2} }{(a+4)(a-4)}=\frac{a+4}{a-4}[/tex]