SOLUTION: combine and simplify a^2/x-1 - a^2/x+1 Thank you

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Question 20898: combine and simplify
a^2/x-1 - a^2/x+1
Thank you
Found 2 solutions by rapaljer, philberg99:
Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
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: %28%28a%5E2%29%2Fx%29+-+1+-+%28%28a%5E2%29%2Fx%29+%2B1+. 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%5E2%2F%28x-1%29+-+a%5E2%2F%28x%2B1%29, which would require a common denominator of %28x-1%29%2A%28x%2B1%29+. You can make this problem slightly EASIER by factoring out a common factor of a%5E2 before doing the LCD.
a%5E2%281%2F%28x-1%29+-+1%2F%28x%2B1%29%29

NOW, do the LCD:
a%5E2%28%281%2F%28x-1%29%29%2A%28%28x%2B1%29%2F%28x%2B1%29%29+-+%281%2F%28x%2B1%29%29%2A%28%28x-1%29%2F%28x-1%29%29%29
a%5E2%28+%28x%2B1%29+-%28x-1%29%29%2F%28%28x-1%29%2A%28x%2B1%29%29

a%5E2+%28+x%2B1+-+x+%2B+1%29+%2F+%28%28x-1%29%2A%28x%2B1%29%29+
a%5E2+%28+2%29+%2F+%28%28x-1%29%2A%28x%2B1%29%29+

2a%5E2++%2F+%28%28x-1%29%2A%28x%2B1%29%29+

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

R^2 at SCC

Answer by philberg99(10) About Me  (Show Source):
You can put this solution on YOUR website!
NO! NO! NO!
You need a common denominator.
%28a%5E2%29%2F%28x-1%29 - %28a%5E2%29%2F%28x%2B1%29
%28%28a%5E2%29%2A%28x%2B1%29%29%2F%28%28x-1%29%2A%28x%2B1%29%29+ - +%28%28a%5E2%29%2A%28x-1%29%29%2F%28%28x%2B1%29%2A%28x-1%29%29
%28a%5E2%2Ax%2Ba%5E2%29%2F%28x%5E2-1%29+ - +%28a%5E2%2Ax-a%5E2%29%2F%28x%5E2-1%29
Now we can subtract the numerators because the denominators are the same. This gives us
%282%2Aa%5E2%29%2F%28x%5E2-1%29