# How do you find the horizontal asymptote for (3x^4 + 2x^2 + 1) / (5x^4 + x -1)?

$\frac{3}{5}$
As $x$ becomes larger and larger the terms other than $\frac{3 {x}^{4}}{5 {x}^{4}}$ become less and less significant.
So ${\lim}_{x \to \pm \infty} f \left(x\right) \to \frac{3 {x}^{4}}{5 {x}^{4}} = \frac{3}{5}$
Note that for both positive and negative $x$ that ${x}^{4}$ is positive.