Rationalizing Denominators

[homeschool mom]

If we write

in the form

such that

,

, and

are positive integers and

is as small as possible, then what is

?

 

[Dr.Peterson]

Please show what you have done, so we can confirm or correct it.

You will first rationalize the denominators of the two fractions, then combine like radicals (e.g. the two terms containing [MATH]\sqrt{5}[/MATH]), and finally combine into a single fraction.

 

[pka]

Hint: \(\sqrt 5+\dfrac{\sqrt 5}{5}=\dfrac{~?~}{5}\)