\(What\,\, is\,\, the\,\, vertical\,\, asymptote,\,\, if\,\, any?\)The vertical asymptote is found by factoring the numerator and denominator as much as you can and then solving for x in the denominator.
\(ex\,\,a.\)
\(y = \dfrac{4x^{2} - 1}{3x(2x + 1)}\)
\(y = \dfrac{(2x - 1)(2x + 1)}{3x(2x + 1)}\)
\(y = \dfrac{2x - 1}{3x}\)
\(3x = 0\)
\(\dfrac{3}{3}x = \dfrac{0}{3}\)
\(x = 0\)
\(so\)
\(x = 0 \,\, is \,\,the\,\,vertical\,\,asymptote\)
