# How do you find the asymptotes for y=(x^3 +3x^2-4x-10)/(x^2-4)?

Consider behaviour in the infinite domain limits and when the denominator goes to zero. The function has three asymptotic lines, $y = x$, $x = - 2$, and $x = + 2$.
In the limit as $x \rightarrow \infty$, $y \rightarrow {x}^{3} / {x}^{2} = x$.
In the limit as $x \rightarrow - \infty$, also $y \rightarrow {x}^{3} / {x}^{2} = x$. So in both infinite domain limits the function tends to the diagonal straight line $y = x$, an asymptote in both cases.
The function has two poles on the real line, at $x = \pm 2$, where the denominator is zero and the numerator is non-zero. So the two lines $x = \pm 2$ are vertical asymptotes of the functions.