Question 143730
{{{40/(2x-3)+30/(4x+5)=-11}}} Start with the given equation



{{{(2x-3)(4x+5)(40/cross(2x-3)+30/cross(4x+5))=-11(2x-3)(4x+5)}}} Multiply both sides by the LCD {{{(2x-3)(4x+5)}}}. This will clear the fractions.




{{{40(4x+5)+30(2x-3)=-11(2x-3)(4x+5)}}} Distribute and multiply



{{{160x+200+60x-90=-11(2x-3)(4x+5)}}} Distribute again



{{{160x+200+60x-90=-11(8x^2-2x-15)}}} Foil



{{{160x+200+60x-90=-88x^2+22x+165}}} Distribute



{{{160x+200+60x-90+88x^2-22x-165=0}}}  Add 88x^2 to both sides.  Subtract 22x from both sides.  Subtract 165 from both sides. 



{{{88x^2+198x-55=0}}} Combine like terms 




{{{11(2x+5)(4x-1)=0}}} Factor the left side 




Now set each factor equal to zero:


{{{2x+5=0}}} or  {{{4x-1=0}}} 


{{{x=-5/2}}} or  {{{x=1/4}}}    Now solve for x in each case



So our answers are


 {{{x=-5/2}}} or  {{{x=1/4}}}