√5+1/√5-1?

Question

Don't know

Answer 1

Should this be
(√5 + 1) / (√5 - 1) ?
If so:-
(√5 +1) (√5 + 1) / (√5 - 1) (√5 + 1)
(5 + 2√5 + 1) / (5 - 1)
(1/4) (6 + 2√5)
(1/2) (3 + √5)

Answer 2

This is a specfic example of the generic question that was asked previously, that is, (√a+√b)/(√a-√b). Using that same method here you need to multiply both the numerator and denominator by √5+1, which will give a result
(5+2√5+1)/(5-1) = (6+2√5)/4 = 2(3+√5)/4 = (3+√5)/2

Answer 3

Of course you want to get the radical out of the denominator.

Multiply the top and bottom by √5+1.
(√5+1)(√5+1) / (√5-1)(√5+1)
(5 + 2√5 + 1) / (5 - 1)
(2√5 + 6)/4
(√5 + 3)/2

Answer 4

You gotta rationalize it first in order to simplify it.
Since you have √5-1 in the deniominator you have to use (√5+1)/(√5+1) in this operation, which is pratically 1. That way you will eliminate the square root in the denominator without changing anything. We shall not use √5+1/√5+1 because, instead of helping, it would complicate even more!

√5+1/√5-1 * √5+1/ √5+1 = (√5+1)(√5+1)/ (√5-1 )(√5+1) = ( 5+2√5 +1)/5-1 = (6+2√5)/4


= (3 +√5)/2

Answer 5

Rationalize the denominator by multiplying the top and bottom by -/5 + 1

Top becomes
(root 5)^2 +2root5 + 1 = 6+ 2root 5

denominator becomes
5-1 = 4

fraction becomes
(6 + 2 -/5)/4

reduced

(3 + -/5)/2

Answer 6

I assume you mean [sqrt(5) + 1] / [sqrt(5) - 1]. We simplify this by rationalizing the base. We multiply the top and bottom of the fraction by [sqrt(5) + 1], and the result is [sqrt(5) + 1]^2 / (5 - 1) = [5 + 2*sqrt(5) + 1] / 4 = [3 + sqrt(5)] / 2.

Answer 7

multiply top and bottom by the conjugate of the denominator

(sqrt(5) + 1) (sqrt (5) + 1) / (sqrt (5) -1) (sqrt (5) + 1)

foil next and diff. of squares on the bottom.

(5 + sqrt(5) + sqrt (5) + 1) / (5 - 1)

6 + 2 sqrt (5) / 4 or reduced 3 + sqrt (5) / 2

Answer 8

Multiply top and bottom by sqrt(5) + 1:
(sqrt(5) + 1)^2 / (sqrt(5) - 1)(sqrt(5) + 1)
= ( 5 + 1 + 2sqrt(5) ) / (5 - 1)
= (6 + 2sqrt(5)) / 4
= (3 + sqrt(5)) / 2.

Answer 9

4/5+2sqrt(5)

Answer 10

Oops...it helps to actually READ the question