SOLUTION: sqrt(2x+3)-sqrt(x+1)=1

Question 97422: sqrt(2x+3)-sqrt(x+1)=1
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
sqrt(2x+3)=sqrt(x+1)+1
Square both sides to get:
2x+3 = (x+1)+2sqrt(x+1) +1
2x+3 = x+2 + 2sqrt(x+1)
x+1 = 2sqrt(x+1)
Square again to gt:
x^2+2x+1 = 4(x+1)
x^2-2x-3=0
(x-3)(x+1)=0
x=3 or x=-1
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Checking answers in sqrt(2x+3)=sqrt(x+1)+1
If x=3: sqrt(9) = sqrt(4)+1
3 = 2+1
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If x=-1: sqrt(1) = sqrt(0)+1
1=1
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Both values of x are valid.
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cheers,
Stan H.
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