Question

Rationalizing the denominator: is it possible to do this one in 1 step?

\[1 \over 1 + \sqrt{3} - \sqrt {5}\]

Answer 1

I did this:
\[\frac{1}{1 + \sqrt{3} - \sqrt{5}} \times \frac{-1+\sqrt{3}-\sqrt{5}}{-1 + \sqrt{3}- \sqrt{5}} = \frac{-1+\sqrt{3}-\sqrt{5}}{7-2\sqrt{15}}\]
Is there a simpler way?

Answer 2

@jackellyn @ajprincess help please!

Answer 3

It looks fine to me, i'm not sure any other way. Sorry.

Answer 4

ya I too am nt sure of any other way..sorry.

Answer 5

let \[a=\sqrt{3}-\sqrt{5}\]
\[1/(1+a)\]
\[1/(1+a)*(1-a)/(1-a)\]
\[(1-a)/(1-a ^{2})\]

Answer 6

or
\[1/(1+\sqrt{3}-\sqrt{5})*(1+\sqrt{3}+\sqrt{5})/(1+\sqrt{3}+\sqrt{5})\]

Answer 7

thanks!