Derivative Rationalizing

mathitup

New member
Joined
Oct 26, 2005
Messages
5
Code:
__1________       -    ___1_____
√(x+h)² - 5             √(x²-5)
________________________________                            
                   h
sorry about that, i hope this helps
I need to find out how to rationalize this
 

pka

Elite Member
Joined
Jan 29, 2005
Messages
9,140
First, simply the fraction \(\displaystyle \frac{{\sqrt {x^2 - 5} - \sqrt {\left( {x + h} \right)^2 - 5} }}{{h\left( {\sqrt {x^2 - 5} } \right)\left( {\sqrt {\left( {x + h} \right)^2 - 5} } \right)}}\).
Then rationalize by multiplying numerator and denominator by \(\displaystyle \sqrt {x^2 - 5} + \sqrt {\left( {x + h} \right)^2 - 5}\)

To help you with formatting, you might consider using TEX.
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mathitup

New member
Joined
Oct 26, 2005
Messages
5
so what happened to the 1's on top in the first part of the question, how were you able to get rid of those?
 

Unco

Senior Member
Joined
Jul 21, 2005
Messages
1,134
Cross multiply.

By the way, if you ever want to get the code tags to work, type it in notepad and copy over - it looks like it should that way.
 

mathitup

New member
Joined
Oct 26, 2005
Messages
5
oh alright thanks alot, so i just cross the top as it was its own equation? and then its all overe h and then i multiply by the roots to rationalize?
 
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