Expert: Socrates - 9/30/2009

Question
what are to rules to rationlizing any futions and/or derivitives

Answer
I assume you are talking about fractions with a binomial in the denominator that has a square root in one or both terms .

Basically, you multiply numerator and denominator by what you get when you change the sign between the terms in the denominator.

Examples,

4/(5+√3) ,  to rationalize , multiply numerator and denominator by 5-√3 . This gives

4(5-√3)/(5+√3)(5-√3)  = 4(5-√3)/22 = 2(5-√3)/11


with algebraic expressions , it is the same basic idea


(2x+1)/(√(3x) - √(2x))  , change the sign between the terms in the denominator and get

(√(3x) + √(2x)) , multiply numerator and denominator by this and get


(2x+1)(√(3x) + √(2x)) / x


one last example


5x/ (√(7x - 1 ) + 5 )

Change the sign between the terms in the denominator and get (√(7x - 1 ) - 5 )

multiply numerator and denominator by (√(7x - 1 ) - 5 ) and get

(5x)(√(7x - 1 ) - 5 ) / (7x - 26)