Evaluate the limit of the function (x^2-1)/(x-1) if x goes to 1?

We'll substitute x by 1 in the expression of the
function:

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

x->1

Since we've
get an indetermination, we can apply L'Hospital's rule:

lim
f(x)/g(x) = lim f'(x)/g'(x)

Let f(x) = x^2 - 1 =>
f'(x) = 2x

Let g(x) = x - 1 => g'(x) =
1

lim (x^2 - 1)/(x-1) = lim
2x/1

x->1                      
x->1

We'll replace x by
1:

lim 2x/1 = 2/1 =
2

The requested limit of the given function,
if x approaches to 1, is lim (x^2 - 1)/(x-1) = 2.