# How do you find the vertical, horizontal and slant asymptotes of #a(x)=(2x^2-1) / (3x^3-2x+1)#?

##### 1 Answer

There is a vertical asymptote at

#### Explanation:

**Step 1.** Find the vertical asymptotes.

Set the denominator equal to zero and solve for

According to the rational root theorem, the rational roots of

So the only possible rational roots are

We have to test all four possibilities.

The only one that works is

So

There is a vertical asymptote at

**Step 2.** Find the horizontal asymptotes.

The degree of the numerator is lower than the degree of the denominator, so the

The horizontal asymptote is at

**Step 3.** Find the slant asymptotes.

A slant asymptote occurs when the degree of the numerator is higher than the degree of the denominator.

Here, the numerator is 2nd degree, and the denominator is 3rd degree, so there are no slant asymptotes.