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

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Question 1132094: The negative reciprocal of the sum of all values of x that satisfy the equation (x-√x+1)/(x+√x+1)=11/5 is...
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


%28x-sqrt%28x%29%2B1%29%2F%28x%2Bsqrt%28x%29%2B1%29=11%2F5
5%28x-sqrt%28x%29%2B1%29=11%28x%2Bsqrt%28x%29%2B1%29
5x-5sqrt%28x%29%2B5=11x%2B11sqrt%28x%29%2B11
0=11x-5x%2B5sqrt%28x%29%2B11sqrt%28x%29%2B11-5
0=6x%2B16sqrt%28x%29%2B6
-%286x%2B6%29=16sqrt%28x%29
-3%28x%2B1%29=8sqrt%28x%29 => no solution exist

but, if you have this:
%28x-sqrt%28x%2B1%29%29%2F%28x%2Bsqrt%28x%2B1%29%29=11%2F5
5%28x-sqrt%28x%2B1%29%29=11%28x%2Bsqrt%28x%2B1%29%29
5x-5sqrt%28x%2B1%29%29=11x%2B11sqrt%28x%2B1%29
5x-11x=11sqrt%28x%2B1%29%2B5sqrt%28x%2B1%29%29
-6x=16sqrt%28x%2B1%29
-6x%2F16=sqrt%28x%2B1%29
-3x%2F8=sqrt%28x%2B1%29
%28-3x%2F8%29%5E2=%28sqrt%28x%2B1%29%29%5E2
9x%5E2%2F64=x%2B1
9x%5E2=64x%2B64
9x%5E2-64x-64=0
%28x+-+8%29+%289+x+%2B+8%29+=+0
x=8
x=-8%2F9
only x=-8%2F9 satisfy %28x-sqrt%28x%2B1%29%29%2F%28x%2Bsqrt%28x%2B1%29%29=11%2F5
The negative reciprocal of the sum of all values of x that satisfy the equation:
the negative reciprocal of x=-8%2F9 is 9%2F8