Question 62272
  
   {{{2/(x^2-4x+3) + 3/(x^2-8x+15) - 6/(x^2-6x+5)}}}  Now let's factorise the denominators as under:
  =  {{{2/(x-3)(x-1)+3/(x-5)(x-3)-6/(x-5)(x-1)}}}
Now, let's take the LCM of the denominators which comes to {{{(x-1)(x-3)(x-5)}}}and simplify the above expression as under:
  
  =  {{{(2(x-5)+3(x-1)-6(x-3))/(x-1)(x-3)(x-5)}}}.  By expanding the numerator, we get
  
  =  {{{(2x-10+3x-3-6x+18)/(x-1)(x-3)(x-5)}}} = {{{(-x+5)/(x-1)(x-3)(x-5)}}}
  
  =  {{{(-1(x-5))/(x-1)(x-3)(x-5)}}} =  {{{(-1*cross((x-5)))/(x-1)(x-3)cross((x-5))}}}
  
  =  {{{(-1)/(x-1)(x-3)}}}.  Answer.  That's all.  I hope this is clear to you. In case of any doubt, feel free to contact me.  All the best.
  
gsm