Question

α²+16/α²-16 + 4/α+4 + 4/α-4

Answer 1

$\frac{a^2+16}{a^2-16}+\frac{4}{a+4}+\frac{4}{a-4}=\\\\=\frac{a^2+16+4(a-4)+4(a+4)}{(a-4)(a+4)}=\\\\=\frac{a^2+8a+16}{(a-4)(a+4)} =\\\\= \frac{(a+4)(a+4)}{(a-4)(a+4)}=\\\\=\frac{a+4}{a-4}$