SOLUTION: Please help me solve this problem: Solve for x: sqrt(x+1)+sqrt(x-1)=sqrt(2x+1)

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Question 640220: Please help me solve this problem: Solve for x: sqrt(x+1)+sqrt(x-1)=sqrt(2x+1)
Answer by josh_jordan(263) About Me  (Show Source):
You can put this solution on YOUR website!
To solve for x, the first thing we want to do is square both sides of our equal sign. This will allow us to get rid of some of the square roots:
%28sqrt%28x%2B1%29%2Bsqrt%28x-1%29%29%5E2+=+sqrt%282x%2B1%29%5E2 =

This reduces down to
x%2B1%2Bsqrt%28x%5E2-1%29%2Bsqrt%28x%5E2-1%29%2B+x-1+=+2x%2B1
Now, let's combine all like terms on each side of the equal sign:
2x%2B2sqrt%28x%5E2-1%29+=+2x+%2B+1
We can now subtract 2x from both sides, that way we will only have the root on the left side:
2x-2x%2B2sqrt%28x%5E2-1%29+=+2x-2x%2B1=
2sqrt%28x%5E2-1%29=1
Now, let's divide both sides by 2, to get rid of the number being multiplied by the square root:
%282sqrt%28x%5E2-1%29%29%2F2=1%2F2=
sqrt%28x%5E2-1%29=1%2F2
We need to get rid of the square root on the left side, so we will square both sides of the equal sign:
%28sqrt%28x%5E2-1%29%29%5E2=%281%2F2%29%5E2=
x%5E2-1=1%2F4
Now, add 1 to both sides:
x%5E2-1%2B1=1%2B%281%2F4%29=
x%5E2=5%2F4
Finally, to get x by itself and solve, we need to take the square root of both sides:
sqrt%28x%5E2%29=sqrt%285%2F4%29=
x+=+sqrt%285%29%2Fsqrt%284%29 =
x+=+sqrt%285%29%2F2