$1 \cdot 14$ Real numbers $a, b$ satisfy $ab=1$, let $M=\frac{1}{1+a}+\frac{1}{1+b}, N=\frac{a}{1+a}+\frac{b}{1+b}$, then the relationship between $M, N$ is
(A) $M>N$.
(B) $M=N$.
(C) $M<N$.
(D) Uncertain.
(China Junior High School Mathematics League, 1996)
[Solution] From the given, we know
$$
M=\frac{1}{1+a}+\frac{1}{1+b}=\frac{b}{b+a b}+\frac{a}{a+a b}=\frac{b}{b+1}+\frac{a}{a+1}=N
$$

Therefore, the correct choice is $(B)$.