Question 107410
I think this is the problem you're trying to solve.
{{{(4x-3)/(3-2x)+5/2=-19/6}}}
{{{(4x-3)/(3-2x)=-19/6-5/2}}}
{{{(4x-3)/(3-2x)=-19/6-15/6}}}
{{{(4x-3)/(3-2x)=-17/3}}}
First step, get rid of the fractions. 
Multiply both sides by the least common denominator, 3(3-2x).
{{{3(3-2x)((4x-3)/(3-2x))=3(3-2x)(-17/3)}}}
{{{3(4x-3)=-17(3-2x)}}}
{{{12x-9=-51+34x}}}
{{{42=22x}}}
{{{x=42/22}}}
{{{highlight(x=21/11)}}}
Check your answer
{{{(4x-3)/(3-2x)+5/2=-19/6}}}
{{{(4(21/11)-3)/(3-2(21/11))+5/2=-19/6}}}
{{{(84/11-3)/(3-42/11)+5/2=-19/6}}}
{{{(84/11-33/11)/(33/11-42/11)+5/2=-19/6}}}
{{{51/(-9)+5/2=-19/6}}}
{{{-204/36+90/36=-114/36}}}
{{{-114/36=-114/36}}}
True statement. Good answer.