SOLUTION: What is the negative reciprocal of the sum of all values of x that satisfy the equation (x-√(x+1))/(x+√(x+1))=11/5?

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Question 1150798: What is the negative reciprocal of the sum of all values of x that satisfy the equation (x-√(x+1))/(x+√(x+1))=11/5?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781) About Me  (Show Source):
Answer by MathTherapy(10552) About Me  (Show Source):
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What is the negative reciprocal of the sum of all values of x that satisfy the equation (x-√(x+1))/(x+√(x+1))=11/5?
When  is solved, matrix%281%2C7%2C+x%2C+%22=%22%2C+-+8%2F9%2C+or%2C+x%2C+%22=%22%2C+8%29

However, x = 8 DOES NOT satisfy the equation, and is therefore considered to be an EXTRANEOUS solution, thereby leaving -+8%2F9 as the SOLE value of x that satisfies the equation.

And, as the sum of the x-values that SATISFY the equation is being sought, the answer is simply the NEGATIVE reciprocal of the SOLE solution, -+8%2F9, which is: highlight_green%289%2F8%29