How do you evaluate the limit #(x^2-7x+10)/(x-2)# as x approaches #2#?

2 Answers
Nov 30, 2016

# :. lim_(x rarr 2) (x^2-7x+10)/(x-2) = -3#

Explanation:

# lim_(x rarr 2) (x^2-7x+10)/(x-2) = lim_(x rarr 2) ((x-5)(x-2))/(x-2)#

When we evaluate the limit we look at the behaviour as #x# approaches #2# and we are not interested in what happens when #x=2# so we can cancel the #(x-2)# factor as #x!=2#

# :. lim_(x rarr 2) (x^2-7x+10)/(x-2) = lim_(x rarr 2) (x-5)#
# :. lim_(x rarr 2) (x^2-7x+10)/(x-2) = (2-5)#
# :. lim_(x rarr 2) (x^2-7x+10)/(x-2) = -3#

Nov 30, 2016

Factor the numerator to simplify the rational function

Explanation:

#x^2-7x+10 = (x-2)(x-5)#

#lim_(x->2) frac (x^2-7x+10) (x-2) = lim_(x->2) frac ((x-2)(x-5)) (x-2)#

#:. = lim_(x->2) (x-5) = -3#