Question

find all vertical asymptotes of the following function.

$$ f ( x ) = \frac { 5 x ^ { 2 } + 9 x - 2 } { 15 x - 3 } $$

Explanation:

Step1: Factor numerator and denominator

Factor numerator \(5x^{2}+9x - 2=(5x - 1)(x + 2)\)
Factor denominator \(15x-3 = 3(5x - 1)\)
So \(f(x)=\frac{(5x - 1)(x + 2)}{3(5x - 1)}\)

Step2: Simplify the function

Cancel out the common factor \((5x - 1)\) (for \(x
eq\frac{1}{5}\)), \(f(x)=\frac{x + 2}{3}\), \(x
eq\frac{1}{5}\)

Answer:

No Vertical Asymptotes