# How do you find the slant asymptote of f(x) = (3x^2 + 2x - 5)/(x - 4)?

Jul 10, 2018

Below

#### Explanation:

When you notice that the degree of your numerator is greater than your denominator, then it is likely that you will need to use long division.

$f \left(x\right) = \frac{3 {x}^{2} + 2 x - 5}{x - 4} = \frac{\left(x - 4\right) \left(3 x + 14\right) + 51}{x - 4} = \left(3 x + 14\right) + \frac{51}{x - 4}$

To find your slant or oblique asymptote, you are finding what happens when x approaches infinity.

When x approaches infinity in the above equation, $\frac{51}{x - 4}$ will approach zero (try putting big numbers into your calculator)

Hence, $f \left(x\right)$ becomes $3 x + 14 + 0 = 3 x + 14$
Therefore, your slant asymptote is $y = 3 x + 14$