Question 22868
{{{((2x-3)/(5x+10))+((3x-2)/(4x+8))=1}}}


This is a rational (fractional!) equation.  First step is to factor those denominators in order to find the LCD for the equation.
{{{((2x-3)/(5(x+2)))+((3x-2)/(4(x+2)))=1}}}


The LCD is 20(x+2) so multiply both sides of the equation by the LCD:
{{{20(x+2)*((2x-3)/(5(x+2)))+20(x+2)*((3x-2)/(4(x+2)))=1*20(x+2)}}}


ALL the denominators divide out!!!
{{{4(2x-3)+5(3x-2) = 20(x+2)}}}
{{{8x - 12 + 15x -10 = 20x +40}}}
{{{23x - 22 = 20x +40}}}

{{{3x = 62}}}
{{{x = 62/3}}}


Ugly answer!  Either it's getting very late or it just didn't come out even!!  Help!! 
Somebody find my error if there is one!!


R^2 at SCC