We have been given a function [tex]f(x)=\frac{x-4}{2x+3}[/tex]. We are asked to find the vertical asymptote of the given rational function.
We know that vertical asymptote of a rational function is the point, where denominator of rational function is equal to zero.
To find vertical asymptote for our given rational function, we will equate denominator with 0 as:
[tex]2x+3=0[/tex]
Let us solve for x.
[tex]2x+3-3=0-3[/tex]
[tex]2x=-3[/tex]
[tex]\frac{2x}{2}=\frac{-3}{2}[/tex]
[tex]x=-\frac{3}{2}[/tex]
Therefore, the vertical symptote of our given rational function is [tex]x=-\frac{3}{2}[/tex].
