A2. For the function $f$, we know that $f(x)=x^{2}+1$. What is $\frac{f(f(x)+x)}{f(x)}$?
(A) $x^{2}+x+1$
(B) $x^{2}+2 x+2$
(C) $x^{2}+1$
(D) $x^{2}+2 x+1$
(E) $x^{2}+x$
A2. If we consider the function $f$, we get $\frac{f(f(x)+x)}{f(x)}=\frac{\left(x^{2}+1+x\right)^{2}+1}{x^{2}+1}=\frac{x^{4}+2 x^{3}+3 x^{2}+2 x+2}{x^{2}+1}$. When we divide the polynomial, we get the result $x^{2}+2 x+2$. The correct answer is therefore $B$.