SOLUTION: Could I please get help with this question. I have tried it many times and come to a complete stop. I think the answer may not exist, but I am not sure. Thank you. x+ (square root

Question 215333: Could I please get help with this question. I have tried it many times and come to a complete stop. I think the answer may not exist, but I am not sure. Thank you.
x+ (square root of x +1) 5
------------------------ = --
x-(square root of x + 1) 11
(equal to 5/11)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
x+ (square root of x +1) 5
------------------------ = --
x-(square root of x + 1) 11
(equal to 5/11)
================================
Cross-multiply to get:
11(x+sqrt(x+1) = 5(x-sqrt(x+1))
11x + 11sqrt(x+1) = 5x-5sqrt(x+1)
6x = -6sqrt(x+1)
x = -sqrt(x+1)
Square both sides to get:
x^2 = x+1
x^2 -x -1 = 0
---
Quadratic Formula:
x = [1 +- sqrt(1 -4*1*-1)]/2
---
x = [1 +- sqrt(5)]/2
Comment: x must be >= 1 to be in the domain of the problem.
---
x = [1 + sqrt(5)]/2 = 1.6180..
====================================
Cheers,
Stan H.
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