Finding Limits Algebraically - Conjugate Method

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...Good day, An alternative way to solve the same indeterminate limit: lim(x-->3)((sqrt(x+3) - sqrt(6))/(x - 3)) (rewrite the denominator x - 3 as: x - 3 = (x + 3) - 6, and then treat this expression as a difference of two squares as follows: x - 3 = (x + 3) - 6 = (sqrt(x+3) - sqrt(6))(sqrt(x+3) + sqrt(6)), replace the denominator x - 3 of the limit by this factored form, and cancel the common factor (sqrt(x+3) - sqrt(6)) of top and bottom, resulting in the solvable limit: lim(x-->3)(1/(sqrt(x+3) + sqrt(6))) = 1/2sqrt(6) = sqrt(6)/12. I hope you appreciate this way too... Take care, Jan-W

jan-willemreens