# Help! The slant asymptote of f(x)=(6x^3-5x^2+3x)/(3x^2-x-14) intersects f where x=?

May 19, 2018

$y = 2 x - 1$

x-int: $x = \frac{1}{2}$

#### Explanation:

Use polynomial division to divide the numerator by the denominator the result is the line that is your slant asymptote.

$\frac{6 {x}^{3} - 5 {x}^{2} + 3 x}{3 {x}^{2} - x - 14}$

6 x^3 - 5 x^2 + 3 x = (2 x - 1) × (3 x^2 - x - 14) + 30 x - 14

so the line $y = 2 x - 1$ is your slant asymptote

the x-int is where $y = 0$:

$0 = 2 x - 1$

$x = \frac{1}{2}$