SOLUTION: please help me with this. (sqrt5) +1/(sqrt5)-1 thanks a bunch

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Question 279164: please help me with this. (sqrt5) +1/(sqrt5)-1 thanks a bunch
Found 2 solutions by Theo, stanbon:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
I think your expression is:

sqrt%285%29+%2B+1%2Fsqrt%285%29+-+1

If so, then:

multiply sqrt%285%29 by sqrt%285%29%2Fsqrt%285%29 to get:

5%2Fsqrt%285%29+%2B+1%2Fsqrt%285%29+-+1 which becomes:

6%2Fsqrt%285%29+-+1

multiply 1 by sqrt%285%29%2Fsqrt%285%29 to get:

6%2Fsqrt%285%29+-+sqrt%285%29%2Fsqrt%285%29 which becomes:

%286+-+sqrt%285%29%29%2Fsqrt%285%29

multiply this by sqrt%285%29%2Fsqrt%285%29 to get:

%286%2Asqrt%285%29+-+5%29%2F5

Verify this is correct by using your calculator to solve the original expression and then using your calculator to solve the final expression.

Both expressions should give you the same answer (they do).


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
please help me with this. (sqrt5) +1/(sqrt5)-1
-----------------------
[sqrt(5)+1]/[sqrt(5)-1]
----
Multiply numerator and denominator by [sqrt(5) +1] to get:
----
[sqrt(5)+1]^2/[5-1]
---
= [5 +(2sqrt(5))+ 1]/4
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= [6 + 2sqrt(5)]/4
---
= [3 + sqrt(5)]/2
==========================
cheers,
Stan H.