How do you find the asymptotes for (x^2+ 3x − 4) /( 4x^2 − 7x + 3)?

Jul 10, 2016

${\lim}_{x \to \pm \infty} y = \frac{1}{4}$

${\lim}_{x \to \frac{3}{4}} y = \pm \infty$

Explanation:

Write as:

$y = \frac{\cancel{\left(x - 1\right)} \left(x + 4\right)}{\cancel{\left(x - 1\right)} \left(4 x - 3\right)} \text{ "=" } \frac{x + 4}{4 x - 3}$

${\lim}_{x \to \pm \infty} y = \frac{1}{4}$

${\lim}_{x \to \frac{3}{4}} y = \pm \infty$