(√(2x+3))-(√(x+1))=1

(√(2x+3))-(√(x+1))=1
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sqrt(2x + 3) - sqrt(x + 1) = 1
[sqrt(2x + 3) - sqrt(x + 1)]^2 = 1^2
(2x + 3) - 2sqrt((2x + 3)(x + 1)) + (x + 1) = 1
(2x + 3 + x + 1) - 2sqrt((2x + 3)(x + 1)) = 1
3x + 4 - 2sqrt((2x + 3)(x + 1)) = 1
3x + 4 - 1 = 2sqrt((2x + 3)(x + 1))
3x + 3 = 2sqrt((2x + 3)(x + 1))
(3x + 3)^2 = [2sqrt((2x + 3)(x + 1))]^2
9(x + 1)^2 = 4(2x + 3)(x + 1)
9(x + 1)^2 - (8x + 12)(x + 1) = 0
(x + 1)[9(x + 1) - (8x + 12)] = 0
(x + 1)[9x + 9 - 8x - 12] = 0
(x + 1)(x - 3) = 0
x + 1 = 0 or x - 3 = 0
x = -1 or x = 3

Hence, x = -1 or x = 3.
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