Final answer:
The vertical asymptote of the rational function g(x)=(5x)/(x+6) is x=-6.
Step-by-step explanation:
The vertical asymptotes of the rational function g(x)=(5x)/(x+6) can be found by determining the values of x that make the denominator, (x+6), equal to zero. Since division by zero is undefined, these values will be the vertical asymptotes.
To find the vertical asymptotes, set the denominator equal to zero and solve for x:
x+6=0
x=-6
Therefore, the vertical asymptote of the rational function is x=-6.