How do you evaluate the limit #(x^2-5x+4)/(x^2-2x-8)# as x approaches #4#?

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Answer 1 · 2016-10-27T20:46:13

Factor both the numerator and the denominator, to see what you can eliminate before substituting.

#=lim_(x -> 4) ((x - 4)(x - 1))/((x - 4)(x + 2))#

#=lim_(x->4) (x - 1)/(x + 2)#

#=(4 - 1)/(4 + 2)#

#= 3/6#

#=1/2#

Hopefully this helps!