# How do you find the asymptotes for #H(x)= (x^3-8) / (x^2-5x+6)#?

##### 1 Answer

We have one vertical asymptotes

#### Explanation:

In algebraic expressions, horizontal asymptotes are where denominator tends to infinity. Here, as denominator is quadratic, we can get up to two horizontal asymptotes.

Further, if highest degree of numerator and denominator are equal, we have vertical asymptote (which is not the case here) and if highest degree of numerator is just one greater than that of denominator, as is the case here, we get a slanting or oblique asymptote.

Now

=

Hence as

Hence, we have horizontal asymptote

Further, as

=

=

Hence as

graph{(y-(x^3-8)/(x^2-5x+6))(y-x-5)=0 [-36.7, 43.3, -10.08, 29.92]}