Will mark brainliest and give 20 points! in what ways can vertical, horizontal, and oblique asymptotes be identified? use your own example to identify.

Vertical asymptote:
When you have a rational expression in which the denominator is zero, you have a vertical asymptote. So to find vertical asymptotes, just set the denominator of your rational expression equal to zero, and then, solve for :

Set the denominator equal to zero:

Solve for :
is the vertical asymptote of our rational expression.

Horizontal asymptote:
Here we have two scenarios.
1) Is the degree of the denominator is higher than the degree of the numerator, you will have a horizontal asymptote at :

Since the degree of the denominator is higher of the degree of the numerator, our rational expression will have an asymptote at 
2) If the degree of both denominator and numerator is the same, the rational expression will have an horizontal asymptote at the ratio of the leading coefficients:

Leading coefficients: 3 and 2
Ratio of leading coefficients:
. Our rational expression will have an horizontal asymptote at 

Oblique asymptote:
If the degree of the numerator is higher than the degree of the numerator, you will have an oblique asymptote. To find it, we are going to perform long division; the quotient (without the remainder) will be the equation of the oblique asymptote line:

The quotient of the long division is  with a remainder of 2; therefore, the equation of the oblique asymptote line will be:

Hello!

the answer is:

the answer is:

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!