SOLUTION: Help please: Divide-- p^2 - q^2/p+q divided by p-q/p+q

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Question 123693: Help please:
Divide--
p^2 - q^2/p+q divided by p-q/p+q
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28p%5E2+-+q%5E2%29%2F%28p%2Bq%29%29%2F%28%28p-q%29%2F%28p%2Bq%29%29


Just like dividing any other fractions, you invert and multiply:

%28%28p%5E2+-+q%5E2%29%2F%28p%2Bq%29%29%2A%28%28p%2Bq%29%2F%28p-q%29%29


%28p%2Bq%29%2F%28p%2Bq%29=1, so:



%28%28p%5E2+-+q%5E2%29%2F%28p-q%29%29

Now, remember the factorization of the difference of two squares: a%5E2-b%5E2=%28a%2Bb%29%28a-b%29

%28%28p%5E2+-+q%5E2%29%2F%28p-q%29%29


%28%28p%2Bq%29%28p-q%29%29%2F%28p-q%29

But %28p-q%29%2F%28p-q%29=1, so

%28%28p%2Bq%29cross%28p-q%29%29%2Fcross%28p-q%29
p%2Bq

Super-double-plus extra credit. %28%28p%5E2+-+q%5E2%29%2F%28p%2Bq%29%29%2F%28%28p-q%29%2F%28p%2Bq%29%29=p%2Bqfor all real numbers p and q with what restriction?