Question 20898
There are actually two ways to interpret this problem, and I noticed that in my first attempt, I missed it both ways!!  It is my privilege in algebra.com to be able to correct my errors!!  I should be so fortunate in the rest of my life!!!


First interpretation:  {{{((a^2)/x) - 1 - ((a^2)/x) +1 }}}.  This was the way I was interepreting it when I first saw this problem, and I missed it.  Interpreted this way, EVERYTHING subtracts out, and the answer would be 0.  


However, now that I look at it again, I think the question was meant to be {{{a^2/(x-1) - a^2/(x+1)}}}, which would require a common denominator of {{{(x-1)*(x+1) }}}.  You can make this problem slightly EASIER by factoring out a common factor of {{{a^2}}} before doing the LCD.  

{{{a^2(1/(x-1) - 1/(x+1))}}}


NOW, do the LCD:
{{{a^2((1/(x-1))*((x+1)/(x+1)) - (1/(x+1))*((x-1)/(x-1)))}}} 

{{{a^2( (x+1) -(x-1))/((x-1)*(x+1))}}}


{{{a^2 ( x+1 - x + 1) / ((x-1)*(x+1)) }}}

{{{a^2 ( 2) / ((x-1)*(x+1)) }}}


{{{2a^2  / ((x-1)*(x+1)) }}}


Does that look better than what I originally posted?  Sorry about that!!  


R^2 at SCC