#lim_(xrarr2)((sqrt(x^2+5)-4x+5)/(x^2-4))#
#lim_(xrarr2)(((sqrt(x^2+5)-(4x-5))(sqrt(x^2+5)+(4x-5)))/((x^2-4)(sqrt(x^2+5)+(4x-5))))# (conjugate both sides)
#lim_(xrarr2)((x^2+5-(4x-5)^2)/((x^2-4)(sqrt(x^2+5)+(4x-5))))#
#lim_(xrarr2)((x^2+5-16x^2+40x-25)/((x^2-4)(sqrt(x^2+5)+(4x-5))))#
#lim_(xrarr2)((-15x^2+40x-20)/((x^2-4)(sqrt(x^2+5)+(4x-5))))#
#lim_(xrarr2)((-5(3x^2-8x+4))/((x^2-4)(sqrt(x^2+5)+(4x-5))))#
#lim_(xrarr2)((-5(3x-2)(x-2))/((x+2)(x-2)(sqrt(x^2+5)+(4x-5))))#
#lim_(xrarr2)((-5(3x-2))/((x+2)(sqrt(x^2+5)+(4x-5))))# (factor out x-2)
direct substitution: #=(-5(3(2)-2))/((2+2)(sqrt(2^2+5)+(4(2)-5)))#
#=(-5(4))/(4(sqrt(9)+3))#
#=-20/(4(6))#
#=-5/6#