How do you rationalize the denominator and simplify #1/(1+sqrt(3)-sqrt(5))#?

1 Answer
A. S. Adikesavan
Mar 30, 2016

#(7+3sqrt3+sqrt5+2sqrt15)/11# = 2.0162, nearly.

Explanation:

Multiply numerator and denominator by #(1+sqrt3+sqrt5)#.
Use #(a+b)(a-b)=(a^2-b^2)# for the denominator.

The denominator now is #(1+sqrt3)^2-(sqrt5)^2= 2sqrt3+1#.

Multiply the numerator and denominator by the conjugate #2sqrt3+1# of the denominator.

Now, the denominator is rationalized to 11.

Expand the product in the numerator and simplify for the answer.

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