Question

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.

$G\left(x\right)=\frac{x^4-1}{x^2-x}$

Short answer

The given rational expression does not have a horizontal or oblique asymptote.

Step-by-step solution

Step 1. Given information

Given rational expression:

$G\left(x\right)=\frac{x^4-1}{x^2-x}$

Step 2. Write the concept

If $n\ge m+2$(the degree of the numerator is two or more greater than the degree of the denominator),

the quotient obtained is a polynomial of degree 2 or higher, and R has neither a horizontal nor an oblique

asymptote. In this case, for very large values of $\left|x\right|$, the graph of R will behave like the graph of the

quotient.

Step 3. Calculation

here$n=4,m=2$

Thus,$n\ge m+2$

Therefore no horizontal or oblique asymptote.