lim x→1<(√(x+3)-2)/(x-1)>
=lim x→1<(√(x+3)-2)(√(x+3)-+2)/(x-1)(√(x+3)+2)>
=lim x→1<(x-1)/(x-1)(√(x+3)+2)>
=lim x→1<1/(√(x+3)+2)>
=1/(√4 +2)
=1/(2+2)
=1/4