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?
<pre>When {{{matrix(1,3, (x - sqrt(x + 1))/(x + sqrt(x + 1)), "=", 11/5)}}} is solved, {{{matrix(1,7, x, "=", - 8/9, or, x, "=", 8)}}}
However, x = 8 <b>DOES NOT</b> satisfy the equation, and is therefore considered to be an EXTRANEOUS solution, thereby leaving {{{- 8/9}}} 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, {{{- 8/9}}}, which is: {{{highlight_green(9/8)}}}