For the function $h(x)=\frac{7 x}{(x+9)(x-2)}$, solve the following inequality.
\[
h(x)< 0
\]
Select the correct choice below and fill in the answer box within your choice.
A. The solution is (Use a comma to separate answers as needed.)
B. The solution is
(Type your answer in interval notation.)
Answer
Therefore, the solution is \(x \in \boxed{(-9,0) \cup (2,\infty)}\).
Step 1 ：First, we need to build a sign chart for the given expression \(\frac{7x}{(x+9)(x-2)}\).
Step 2 ：The sign chart is as follows: \[\begin{array}{c|cccc} & x < -9 & -9 < x < 0 & 0 < x < 2 & 2 < x \\ \hline 7x & - & - & + & + \\ x + 9 & - & + & + & + \\ x - 2 & - & - & - & + \\ \frac{7x}{(x+9)(x-2)} & + & - & + & - \end{array}\]
Step 3 ：From the sign chart, we can see that the expression is positive when \(x\) is in the interval \((-9,0)\) and \((2,\infty)\).
Step 4 ：Therefore, the solution is \(x \in \boxed{(-9,0) \cup (2,\infty)}\).
