Question

1//(a+1)+(2a-10)//(a^2-a-2)+a//(a-2)

Answer 1

$frac{1}{a+1}+frac{2a-10}{a^2-a-2}+frac{a}{a-2}=frac{1}{a+1}+frac{2a-10}{(a+1)(a-2)}+frac{a}{a-2}=frac{a-2+2a-10+a(a+1)}{(a+1)(a-2)}$

$=frac{3a-12+a^2+a}{(a+1)(a-2)}=frac{a^2+4a-12}{(a+1)(a-2)}=frac{(a+6)(a-2)}{(a+1)(a-2)}=frac{a+6}{a+1}$