Algebraic conversion of LHS to RHS equation

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SUMMARY

The discussion focuses on converting the left-hand side (LHS) of the equation involving square roots and a variable 'h' to match the right-hand side (RHS). The equation presented is from Wolfram Alpha. The user attempted to manipulate the equation by factoring and finding common denominators but reached a dead end. The solution was ultimately clarified by a user who referenced the identity (a-b)(a+b) = a²-b², leading to a successful conversion.

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Homework Statement



I'm having trouble converting the LHS to the RHS of this equation:

http://www.wolframalpha.com/input/?i=%281%2F%28sqrt%285+%2B+h%29+%29-+1%2F%28sqrt%285%29%29%29%2Fh+%3D+-1%2F%28%28sqrt%285%29*sqrt%285%2Bh%29%29*%28sqrt%285%2Bh%29+%2B+sqrt%285%29%29%29

Homework Equations



N/A

The Attempt at a Solution



I've tried a bunch of different things. One thing I tried was bringing the h in the denominator to the denominators of the numerators (i.e. making it a factor of the numerators' denominators). With common denominators and factoring out h I end up getting:

[urlhttp://www.wolframalpha.com/input/?i=%28sqrt%285%29+-+sqrt%285%2Bh%29%29%2F%28h*%28sqrt%285%2Bh%29*sqrt%285%29%29%29[/url]

...And I'm stuck there. I would appreciate if someone could just show me step-by-step the solution (working the LHS to meet the RHS please).
 
Last edited:
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What is the problem?

ehild
 
(a-b)(a+b) = a^2-b^2 and a = \sqrt{a} \sqrt{a}.
 
I got it, thanks all.
 

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