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

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Answer

Therefore, the solution is $x \in (- 9, 0) \cup (2, \infty)$ .

Steps

Step 1 ：First, we need to build a sign chart for the given expression $\frac{7 x}{(x + 9) (x - 2)}$ .

Step 2 ：The sign chart is as follows: $\begin{array}{ccccc} x < - 9 & - 9 < x < 0 & 0 < x < 2 & 2 < x \\ 7 x & - & - & + & + \\ x + 9 & - & + & + & + \\ x - 2 & - & - & - & + \\ \frac{7 x}{(x + 9) (x - 2)} & + & - & + & - \end{array}$

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 $x \in (- 9, 0) \cup (2, \infty)$ .

For the function h(x)=7x(x+9)(x−2), solve the following inequality.h(x)<0Select 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

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