Find the equation of all vertical asymptotes of the following function. f(x)=(2x-6)/(x^2)-4x-12 Answer Attempt 2 out of 2 square

To find the vertical asymptotes of the function $f(x)=\frac {2x-6}{x^{2}-4x-12}$, we need to determine the values of $x$ for which the denominator is equal to zero, as these are the points where the function is undefined.<br /><br />The denominator of the function is $x^{2}-4x-12$. To find the values of $x$ that make the denominator zero, we can factor the quadratic expression:<br /><br />$x^{2}-4x-12 = (x-6)(x+2)$<br /><br />Setting each factor equal to zero gives us the values of $x$ that make the denominator zero:<br /><br />$x-6=0$ or $x+2=0$<br /><br />Solving for $x$, we get:<br /><br />$x=6$ or $x=-2$<br /><br />Therefore, the function $f(x)=\frac {2x-6}{x^{2}-4x-12}$ has vertical asymptotes at $x=6$ and $x=-2$.