Rationalize the denominator?

Question

1 / ( 1+√3-√5)

Answer 1

i would treat  1+√3 = a

then 1/(a - √5) = (a + √5)/( a- 5) = (a + √5)/(√3-4)

= ( 1+√3+√5)((√3+4)/ (√3-4)(√3+4)

= ( 1+√3+√5)((√3+4)/ (-1)

= - ( 1+√3+√5)((4+√3)

= - (4+4√3+4√5+√3 + 3 + +√15)

= - 7 - 5√3 - 4√5 -√15

Answer 2

I think you have to do two steps here.  In the cases you usually see, you know that if the denom is:

1/(1+sqrt(x))

you know that you multiply num and denom by 1-sqrt(x)

here, we have 1+sqrt(3)-sqrt(5) in the denom, so we first multiply num

and denom by

1-sqrt(3)+sqrt(5)

this will give you a denom of -7+sqrt(15)

you now multiply num and denom of the new fraction by

-7-sqrt(15)

and you will have rationalized your fraction

  

Answer 3

1/(1+√-√5)   *   (1-√5+√5)/(1-√5+√5)

You basically reverse the signs of the denominator and times it