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Evaluate the following limit: underset( ...

Evaluate the following limit: `underset( x rarr 3) ( "lim")(sqrt(x+3)-sqrt(6))/(x^2-9)`

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`(lim)_(x->3)(sqrt(x+3)-sqrt(6))/(x^2-9)`

Multiplying with conjugate:

`(lim)_(x->3)(x+3-6)/((x^2-9)(sqrt(x+3)+sqrt(6))`

`(lim)_(x->3)(x-3)/((x-3)(x+3)(sqrt(x+3)+sqrt(6))`

`(lim)_(x->3)(1)/((x+3)(sqrt(x+3)+sqrt(6))`

`=(1)/((3+3)(sqrt(3+3)+sqrt(6))`

`=(1)/(12sqrt(6)`

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