Lim x^2 - 2x / x^2 - 5x + 6 ? X=>2

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Answer 1 · 2018-03-13T09:44:18

#-2#

Not absolutely sure if this is the right expression:

#(x^2-2x)/(x^2-5x+6)#

Factor numerator and denominator:

#(x(x-2))/((x-3)(x-2))#

Cancel like factors:

#(xcancel((x-2)))/((x-3)cancel((x-2)))#

#x/(x-3)#

Plug in #x=2#

#2/((2)-3)=-2#

So:

#lim_(x->2)((x^2-2x)/(x^2-5x+6))=-2#