**Find the vertical asymptotes, if any, and the values of x corresponding to holes:** Best answer & explanation are below. Here, are the detailed description.

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**Find the vertical asymptotes, if any, and the values of x corresponding to holes**

**Find the vertical asymptotes, if any, and the value of x corresponding to holes, if any, of the graph of the following rational function.** f(x) =x-3 / x²-9 ….. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an integer or a fraction. Use a comma to separate answers as needed.)

**A.**There are no vertical asymptotes but there is (are) hole(s) corresponding to x =**B.**Vertical asymptote(s) at x= There are no holes.**C.**Vertical asymptote(s) at x= and hole(s) corresponding to x =**D.**There are no discontinuities.

**Final answer:** The vertical **asymptote **of the given rational function is x=-3 and there is a hole at x=3.

**Best Explanation:**

To find the **vertical asymptotes** and the value of x corresponding to **holes**, we need to *factor* the *numerator* and *denominator* of the *rational function*.

- Given function: f(x) = (x-3) / (x²-9)

- Factoring the numerator: x-3

- Factoring the denominator: (x+3)(x-3)

- The denominator has a factor of (x-3), which means there is a hole at x=3.

- The denominator also has a factor of (x+3), which means there is a vertical asymptote at x=-3.

- Therefore, the correct choice is C. Vertical asymptote(s) at x=-3 and hole(s) corresponding to x=3.

Find the vertical asymptotes, if any, and the values of x corresponding to holes – video are below: