1. Define the operation symbol “ * ” as: $a * b=$ $\frac{a+b}{a b}$ (where $a$ and $b$ are not 0). There are two conclusions below:
(1) The operation “ * ” satisfies the commutative law;
(2) The operation “ * ” satisfies the associative law.
Among them ( ).
(A) Only (1) is correct
(B) Only (2) is correct
(C) Both (1) and (2) are correct
(D) Neither (1) nor (2) is correct
1.A.
From $a * b=\frac{a+b}{a b}=\frac{1}{a}+\frac{1}{b}$, it is easy to see that the operation “*” satisfies the commutative law.
$$
\begin{array}{l}
\text { and } a *(b+c)=\frac{1}{a}+\frac{1}{b+c}, \\
a * b+a * c=\frac{1}{a}+\frac{1}{b}+\frac{1}{a}+\frac{1}{c},
\end{array}
$$

By the arbitrariness of $a$, we can see that the operation “*” does not satisfy the associative law.