If $\frac{d}{dx}\left[\frac{1+x^2+x^4}{1+x+x^2}\right]=ax+b$, then $(a,b)=$

$\frac{d}{dx}\left[\frac{1+x^2+x^4}{1+x+x^2}\right]=ax+b$

$\frac{d}{dx}\left[\frac{{(x^2+1)}^2-x^2}{1+x+x^2}\right]=ax+b$

$\frac{d}{dx}\left[\frac{(x^2+1+x)(x^2+1-x)}{(1+x+x^2)}\right]=ax+b$

$\Rightarrow 2x-1=ax+b$

$a=2,b=-1$

$(a,b)=(2,-1)$