Assume $\lim _{x \rightarrow 1} f(x)=12$ and $\lim _{x \rightarrow 1} g(x)=3$. Compute the following limit and state the limit laws used to justify the computation. \[ \lim _{x \rightarrow 1}(f(x)-g(x)) \]

Step 1 ：Assume \(\lim _{x \rightarrow 1} f(x)=12\) and \(\lim _{x \rightarrow 1} g(x)=3\). We are asked to compute the following limit and state the limit laws used to justify the computation: \(\lim _{x \rightarrow 1}(f(x)-g(x))\).

Step 2 ：The limit of the difference of two functions is the difference of their limits, provided both limits exist. This is known as the limit law for difference.

Step 3 ：In this case, we know that both \(\lim _{x \rightarrow 1} f(x)\) and \(\lim _{x \rightarrow 1} g(x)\) exist and are given as 12 and 3 respectively.

Step 4 ：Therefore, we can use the limit law for difference to compute the limit of the difference of the two functions.

Step 5 ：Subtract the limit of g(x) from the limit of f(x): \(12 - 3 = 9\).

Step 6 ：Final Answer: The limit of the difference of the two functions as x approaches 1 is \(\boxed{9}\).