Find the limit of the function (x^2+2x-3)/|x-1| if x approaches 1 from the left.

We are searching for the limit of the function for the
values of x that are smaller than 1.

So,
x<1.

We'll subtract 1 both
sides:

x - 1<0

If x -
1<0 => |x-1| = -(x-1)

We'll substitute the
denominator by -(x-1) and we'll factorize the
numerator:

lim
(x-1)(x+3)/-(x-1)

We'll simplify and we'll
obtain:

lim -(x+3)

We'll
substitute x by 1 and we'll get:

lim -(x+3) = -(1+3) =
-4

The limit of the function, when x
approaches to 1 from the left, is lim (x^2+2x-3)/|x-1| =
-4.