# How do you find vertical, horizontal and oblique asymptotes for #(x^2 - 9)/(3x-6)#?

##### 1 Answer

**Vertical Asymptote: **

**Horizontal Asymptote: ** None

**Equation of the Slant/Oblique Asymptote: **

#### Explanation:

**Given:**

To find the **Vertical Asymptote:**

**a. Factor where possible**

**b. Cancel common factors, if any**

**c. Set Denominator = 0**

We will start following the steps:

**Consider:**

We will factor where possible:

If there are any **common factors** in the numerator and the denominator, we can **cancel** them.

But, we do not have any.

Hence, we will move on.

Next, we set the denominator to zero.

Add

Hence, our **Vertical Asymptote is at**

Refer to the graph below:

To find the **Horizontal Asymptote:**

**Consider:**

Since the **highest degree of the numerator is greater than the highest degree of the denominator**,

**Horizontal Asymptote DOES NOT EXIST**

To find the **Slant/Oblique Asymptote:**

**Consider:**

Since, the **highest degree of the numerator** is **one more than the highest degree of the denominator**, we do have a **Slant/Oblique Asymptote**

We will now perform the **Polynomial Long Division** using

Hence, the **Result of our Long Polynomial Division is**

**Equation of the Slant/Oblique Asymptote is**

Refer to the graph below:

We have all the required results now.