simplify a^2-1/a^2+2a-3

First, you need to put the numerator and denominator
within brackets, such as:

3))

We notice that the numerator is a difference of two
squares that returns the special product:

(a-1)(a+1)

We'll decompose the denominator in it's
factors. For this reason, we'll apply the quadratic formula, to determine the roots of
the expression from denominator.

a1 = (-2+
)/2

a1 = (-2+4)/2

a1 =
1

a2 = (-2-4)/2

a2 =
-3

The denominator could be written as a product of linear
factors:

3)

We'll re-write the given
expression:

=

We'll reduce the
fraction and we'll get:

- 1))/((a^2 + 2a - 3)) = ((a + 1))/((a+3))