Solution
Step 1
Horizontal Asymptotes of Rational Functions
The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.
If N is the degree of the numerator and D is the degree of the denominator, and…
N < D, then the horizontal asymptote is y = 0.
N = D, then the horizontal asymptote is y = ratio of leading coefficients.
N > D, then there is no horizontal asymptote.
Step 2
Identify Vertical Asymptotes of a Rational Function
Factor the numerator and denominator.
Simplify by canceling common factors in the numerator and the denominator.
Set the simplified denominator equal to zero and solve for x.
Step 3
x = 2 and x = 1
x - 2 and x - 1
The denominator expression will be (x-2)(x-1)
Step 4
[tex]\begin{gathered} The\text{ rational fraction is} \\ \\ y=\frac{1}{(x-2)(x-1)} \end{gathered}[/tex]Final answer
[tex]y\text{ = }\frac{1}{(x-2)(x-1)}[/tex]