Question 432481
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Hi
Re: LCD
 My recommendation would be: 
 In order to quickly proceed with the simplification
  1) Note the basic facts as to the factors in the denominators
     For ex:  3/X + 4/Y = (3Y + 4X)/XY    
  2) |X and Y can be 'anything' for example: 
    {{{3/(x+1) + 4/(x+2) = (3(x+2) + 4(x+1))/(x+1)(x+2) = (7x+10)/((x+1)(x+2))}}}
 
Always important to proceed using basic principles:
   3/4 + 4/12 does equal (3*12 + 4*4)/48 = 52/48 = 13/12 
Yes, had we used 12 to begin with, rather than the product, 48:
     (9 + 4)/12 = 13/12 would have been 'simpler' which is the point of the LCD
However, there is no excuse really, not to push one's pencil using the basics.
Many times the product of the denominators is just fine to use, my experience.
With experience, the LCD will "pop into one's head" more easily.