SOLUTION: Rationalize the denominator.. {{{((sqrt(a+b))+(sqrt(a-b)))/((sqrt(a+b))-(sqrt(a-b)))}}}

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Question 866784: Rationalize the denominator..



Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A=sqrt%28a%2Bb%29 and B=sqrt%28a-b%29
%28A%2BB%29%2F%28A-B%29=%28%28A%2BB%29%2F%28A-B%29%29%2A%28%28A%2BB%29%2F%28A%2BB%29%29
%28A%2BB%29%2F%28A-B%29=%28A%5E2%2B2AB%2BB%5E2%29%2F%28A%5E2-B%5E2%29
.
.
A%5E2=a%2Bb
B%5E2=a-b
A%5E2-B%5E2=2b
2AB=2sqrt%28%28a%2Bb%29%28a-b%29%29=2sqrt%28a%5E2-b%5E2%29}

Putting it all together,
%28A%2BB%29%2F%28A-B%29=%282%28a%2Bsqrt%28a%5E2-b%5E2%29%29%29%2F%282b%29
%28A%2BB%29%2F%28A-B%29=%28a%2Bsqrt%28a%5E2-b%5E2%29%29%2F%28b%29