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

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

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

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

`a^2 - 1 =
(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+`sqrt(4 + 12)`
)/2

a1 = (-2+4)/2

a1 =
1

a2 = (-2-4)/2

a2 =
-3

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

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

We'll re-write the given
expression:

`((a^2 - 1))/((a^2 + 2a - 3))` =
`[(a-1)(a+1)]/[(a-1)(a+3)]`

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

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