Question

СРОЧНО. Даю 60 баллов.

Answer 1

$\frac{1}{(a-1)(a-2)}+\frac{1}{(a-2)(a-3)}+\frac{1}{(a-3)(a-4)}=\frac{(a-3)(a-4)+(a-1)(a-4)+(a-1)(a-2)}{(a-1)(a-2)(a-3)(a-4)}=\\\\=\frac{a^{2}-7a+12+a^{2}-5a+4+a^{2}-3a+2}{(a-1)(a-2)(a-3)(a-4)}=\frac{3a^{2}-15a+18 }{(a-1)(a-2)(a-3)(a-4)}=\frac{3(a^{2}-5a+6) }{(a-1)(a-2)(a-3)(a-4)}=\\\\=\frac{3(a-2)(a-3)}{(a-1)(a-2)(a-3)(a-4)}=\frac{3}{(a-1)(a-4)}$