How do you find the limit of #(x^2-1)/(x-1)# as #x# approaches 1?

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Answer 1 · 2015-07-15T18:11:23

#lim_{xto1}(x^2-1)/(x-1) = lim_{xto1}x+1 = 2#

Let's try direct substitution.

#(x^2-1)/(x-1) = (1^2-1)/(1-1) = (1-1)/0= 0/0#

Direct substitution doesn't work. Let's try factoring.

#(x^2-1)/(x-1) = ((x+1)(x-1))/(x-1) = x+ 1#

Now try direct substitution again.

#x+1 = 1+1 = 2#

#lim_{xto1}(x^2-1)/(x-1) = lim_{xto1}x+1 = 2#