lim(x→3) [√(2x+3)-3]/[√(x+1)+2]
=lim(x→3) [√(2x+3)-3]'/[√(x+1)+2]'
=lim(x→3) [1/√(2x+3)]/[1/2√(x+1)]
=lim(x→3) [2√(x+1)/√(2x+3)]
=2√4/√9
=4/3