let's recall that a rational whose numerator and denominator are of the same degree, has a horizontal asymptote at the fraction provided by the leading term's coefficients.
so we can simply pick any two polynomials, make them the same degree and give their leading term 2 and 9 respectively.
hmmmm say for the numerator x⁴ - 3x³.... and the denominator hmm say x⁴ + 7x, so then let's give them 2 and 9 respective... so
[tex]\bf \cfrac{\stackrel{\stackrel{\textit{leading term}}{\downarrow }}{2x^4}-3x^3}{\underset{\underset{\textit{leading term}}{\uparrow }}{9x^4}+7x}\implies \stackrel{\textit{horizontal asymptote}}{y=\cfrac{2}{9}}[/tex]
