How do you rationalize the denominator and simplify #1/(sqrt5-3)#?

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How do you rationalize the denominator and simplify #1/(sqrt5-3)#?

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Answer 1 · 2016-05-03T15:13:36

#1/(sqrt(5)-3)=-(sqrt(5)+3)/4#

Explanation:

For expressions #text(something)/(sqrt(a)-b)# we multiply the numerator and denominator by #sqrt(a)+b# so it matches the LHS of the formula #(x+y)(x-y)=x^2-y^2#.

#1/(sqrt(5)-3)=1/(sqrt(5)-3) * (sqrt(5)+3)/(sqrt(5)+3)=(sqrt(5)+3)/(5-9)=-(sqrt(5)+3)/4#

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How do you rationalize the denominator and simplify #1/(sqrt5-3)#?

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