SOLUTION: If 1/R=1/r1+1/r2; find r2

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Question 51315: If 1/R=1/r1+1/r2; find r2
Found 2 solutions by Nate, rapaljer:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
1/R = 1/r1 + 1/r2
1/R - 1/r1 = 1/r2
(1/R - 1/r1)^-1 = r2
I think you can futher simplify.

Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
First of all, let me congratulate you on a GREAT question!! This question (or one just about like it!) is probably in EVERY algebra book in the country!! Here it is:
1%2FR+=+1%2Fr%5B1%5D+%2B+1%2Fr%5B2%5D

Multiply both sides of the equation by the LCD, which is R%2Ar%5B1%5D%2Ar%5B2%5D+.
R%2Ar%5B1%5D%2Ar%5B2%5D%2A%281%2FR%29+=+R%2Ar%5B1%5D%2Ar%5B2%5D%2A%281%2Fr%5B1%5D%29+%2B+R%2Ar%5B1%5D%2Ar%5B2%5D%2A%281%2Fr%5B2%5D%29

The denominators all divide out, leaving this:
r%5B1%5D%2Ar%5B2%5D+=+R%2Ar%5B2%5D+%2B+R%2Ar%5B1%5D

Get all the r%5B2%5D terms on the left side by subtracting R%2Ar%5B2%5D+ from each side:
r%5B1%5D%2Ar%5B2%5D+-+R%2Ar%5B2%5D+=+R%2Ar%5B1%5D

Get the r%5B2%5D+ in one place, by factoring out the common factor, which is r%5B2%5D.
r%5B2%5D%2A%28r%5B1%5D+-+R%29+=+R%2Ar%5B1%5D

Divide both sides by r%5B1%5D
%28r%5B2%5D%2A%28r%5B1%5D+-+R%29%29%2F%28r%5B1%5D+-+R%29+=+%28R%2Ar%5B1%5D%29%2F%28r%5B1%5D+-+R%29
r%5B2%5D+=+%28R%2Ar%5B1%5D%29%2F%28r%5B1%5D+-+R%29

R^2 at SCC