Question 215333
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.