Question

Simplify the following expression fully:

$\frac{x^3+1}{x^2-x+1}-\frac{4x^2-3x-1}{4x+1}$

Answer 1

x^3+1=(x+1) (x^2-x+1)
so  
(x^3+1)/(x^2-x+1)=x+1.............................(1)
now
4x^2-3x-1=4x^2-4x+x-1
              =4x(x-1)+1(x-1)
               =(x-1)(4x+1)
so
(4x^2-3x-1)/4x+1=(x-1).........................(2)
so      
= x+1-x+1=2