determine the vertical asymptotes of the graph of the function. give your answers as equations in exact…

determine the vertical asymptotes of the graph of the function. give your answers as equations in exact form. g(t)=(t² - 1)/(3t² + 4t - 3) separate multiple equations with commas as necessary. select \none\ if applicable. equation(s) of the vertical asymptote(s):

determine the vertical asymptotes of the graph of the function. give your answers as equations in exact form. g(t)=(t² - 1)/(3t² + 4t - 3) separate multiple equations with commas as necessary. select \none\ if applicable. equation(s) of the vertical asymptote(s):

Answer

Explanation:

Step1: Find when denominator is 0

Set $3t^{2}+4t - 3=0$.

Step2: Use quadratic formula

For $at^{2}+bt + c = 0$ ($a = 3$, $b = 4$, $c=-3$), $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. So $t=\frac{-4\pm\sqrt{4^{2}-4\times3\times(-3)}}{2\times3}=\frac{-4\pm\sqrt{16 + 36}}{6}=\frac{-4\pm\sqrt{52}}{6}=\frac{-4\pm2\sqrt{13}}{6}=\frac{-2\pm\sqrt{13}}{3}$.

Answer:

$t=\frac{-2+\sqrt{13}}{3},t=\frac{-2 - \sqrt{13}}{3}$