Question

упростите выражение 2/a+2/a+2-4a/a2-4

Answer 1

$\frac{2}{a}+\frac{2}{a+2}-\frac{4a}{a^{2}-4}=\frac{2}{a}+\frac{2}{a+2}-\frac{4a}{(a-2)(a+2)}=\frac{2*(a^{2}-4)+2*a*(a-2)-4a*a }{a(a-2)(a+2)}=\\\\=\frac{2a^{2}-8+2a^{2}-4a-4a^{2}}{a(a-2)(a+2)}=\frac{-4a-8}{a(a-2)(a+2)} =\frac{-4(a+2)}{a(a-2)(a+2)}=\frac{-4}{a(a-2)}=\frac{4}{a(2-a)}=\frac{4}{2a-a^{2}} \\\\Otvet:\boxed{\frac{4}{2a-a^{2}}}$