Question 801871
given: {{{g(x)=((2x-1)(x+2))/((2x+3)(3x-4))) }}} 

Vertical asymptote are zeros  of denominator {{{((2x+3)(3x-4)) }}}.

set the denominator to zero and solve for {{{x}}}:

{{{(2x+3)(3x-4)=0}}} ....it will be equal to zero if either {{{(2x+3)=0}}} or {{{ (3x-4)=0}}}

if {{{(2x+3)=0}}}=> {{{2x =-3}}}=> {{{x =-3/2}}}=> {{{x =-1.5}}}

if {{{ (3x-4)=0}}}=>{{{ 3x=4}}}=>{{{ x=4/3}}}=>=>{{{ x=1.33}}}



{{{drawing(600, 600, -10, 10, -10, 10,  blue(line(-1.5,10,-1.5,-10)),blue(line(1.33,10,1.33,-10)), grid(0),
graph( 600, 600, -10, 10, -10, 10, ((2x-1)(x+2))/((2x+3)(3x-4)))) }}}