Please simplify the expression below:

Question

(4a²+3a+2)/(a³-1)-(1-2a)/(a²+a+1)

Answer 1

(4a²+3a+2)/(a³-1)-(1-2a)/(a²+a+1)=

= (4a²+3a+2)/((a-1)(a²+a+1))-(1-2a)/(a²+a+1)=

=(1/(a²+a+1)) ((4a²+3a+2)/(a-1)-1+2a))=

=(1/(a²+a+1)) ((4a²+3a+2-a+1+2a²-2a)/(a-1))

=(1/(a²+a+1)) ((6a²+3)/(a-1))

=3(2a²+1)/(a³-1).