SOLUTION: {{{sqrt(2x+3)-sqrt(x+1)=1}}} can someone explain this problem to me?

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Question 157511: can someone explain this problem to me?
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


Isolate one of the square root terms on one side
of the equation.  I will isolate the first term, 
by adding  to both sides:



Square both sides:



The left side amounts to squaring a square root,
which just amounts to taking away the radical.

The right side is not so easy.  Write  as 
and use FOIL:





Combine the two middle terms, which are like terms, 
on the right:



Simplify



Isolate the radical term on the left:



Simplify:



Square both sides:









Get 0 on the left:





Switch sides:





Set each factor = 0

 gives 

 gives 

But we must check these because
many times we get extraneous solutions:

Checking  in original:













Therefore  is a solution.

But we must check these because
many times we get extraneous solutions:

Checking  in original:













Therefore  is also a solution.

Edwin

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