limx→3√x+3−√6x2−9
Rationalising the numenator
=limx→3(√x+3−√6)(x−3)(x+3)(√x+3−√6)(√x+3+√6)
=limx→3((x+3)−6)(x−3)(x+3)(√x+3+√6)
=limx→3(x−3)(x−3)(x+3)(√x+3+√6)
=limx→31(x+3)(√x+3+√6)
=1(3+3)√3+3+√6
=16(√6+√6)=16×2√6
=112√6