Find the vertical asymptote. \( g(x)=\frac{(x+3)(x-2)}{(x+5)(2 x-1)} \) \( x=-5 \) Sclect all correct options \( x=-1 / 2 \)

A vertical asymptote occurs when the denominator of a rational function approaches zero while the numerator does not at the same x-value. In the function \( g(x)=\frac{(x+3)(x-2)}{(x+5)(2x-1)} \), we can see that the denominator is zero when \( x = -5 \) and \( x = \frac{1}{2} \). Thus, both \( x = -5 \) and \( x = -\frac{1}{2} \) are vertical asymptotes. Remember, we’re looking for values that make the denominator zero while ensuring that the numerator doesn’t also equal zero at those same x-values. In this case, since \( g(-5) \) produces a valid asymptote, it’s a go-to point. However, \( g(-\frac{1}{2}) \) should also be checked for clarity: the numerator does not equal zero, confirming that \( x = -\frac{1}{2} \) is also a vertical asymptote!