3. Let $x+y=1$. If
$$
M=\frac{x^{100}}{x^{2}+y}+\frac{y^{2}}{x+y^{2}}, N=\frac{x^{100}}{x+y^{2}}+\frac{y^{2}}{x^{2}+y} \text {, }
$$

then the relationship between $M$ and $N$ is $($ ).
(A) $M>N$
(B) $M=N$
(C) $M<N$
(D) Cannot be determined
3. B.

Given $x+y=1$, we have
$$
\begin{array}{l}
x^{2}+y=x^{2}-x+(x+y)=1-x y, \\
x+y^{2}=(x+y)-y+y^{2}=1-x y .
\end{array}
$$

Thus, $M=N=\frac{x^{100}+y^{2}}{1-x y}$.
Note: When $x+y=1$, the equation $t^{2}-t+1=0$ has no solution, so $x y \neq 1$. Therefore, the denominator is not 0.