SOLUTION: Find all solutions of sqrt(x+10)-(6/sqrt(x+10)=5

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Question 702144: Find all solutions of
sqrt(x+10)-(6/sqrt(x+10)=5
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B10%29-6%2Fsqrt%28x%2B10%29=5 is asking for a change of variable with y=sqrt%28x%2B10%29
The equation transforms into
y-6%2Fy=5
Multiplying both sides of the equation time y,
we do not lose any solution.
Any solution we gain can be eliminated later.
Multiplying both sides of the equation time y we get
y%5E2-6=5y --> y%5E2-5y-6=0
Factoring, we get %28y-6%29%28y%2B1%29=0
The solutions to that equation are y=-1 and y=6.
They are both solutions of y-6%2Fy=5,
but y=sqrt%28x%2B10%29 is by definition a positive number,
so we eliminate y=-1 as a solution.
We continue with sqrt%28x%2B10%29=6 --> x%2B10=6%5E2 --> x%2B10=36
x%2B10=36 --> x=36-10 --> highlight%28x=26%29