Question 201334
{{{3/(-5-x)-x/(x-3) = 0}}}

Multiply equation by LCD (-5-x)(x-3). This gives us: 

3(x-3) – x(-5-x) = 0(-5-x)(x-3) =  {{{3x-9+5x+x^2 = 0}}}


{{{3x-9+5x+x^2 = 0}}}  =  {{{x^2 + 8x - 9 = 0}}}

(x + 9)(x – 1) = 0


Therefore, x = - 9 or 1, or {- 9, 1}.


Checking, when x = - 9

{{{3/(-5-x)-x/(x-3) = 0}}}   =   {{{3/(-5-(-9))--9/(-9-3) = 0}}}



{{{3/(-5+9)+9/(-12) = 0}}}  =  {{{3/4+9/(-12) = 0}}}  


Multiply equation by LCD, - 12
-3(3) + 1(9), or, -9 + 9 = 0 (TRUE)


Checking, when x = 1

{{{3/(-5-x)-x/(x-3) = 0}}}   =   {{{3/(-5-1)-1/(1-3) = 0}}}


{{{3/(-5-1)-1/(1-3) = 0}}}  =  {{{3/-6-1/-2 = 0}}}  


Multiply equation by LCD, - 6
1(3) – 3(1)  =  0, or, 3 – 3 = 0 (TRUE)