Question about reducing a square root.

ozone
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IDK if this should be in the precalc section, but I was wondering how to reduce

\sqrt{(3+\sqrt{5})} / \sqrt{(3-\sqrt{5})} to (\sqrt{5} + 1) /(\sqrt{5} - 1)
 
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Notice that 3±√5=0.5(6±2√5)=.5(5±2√5+1)=...

ehild
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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