Simplify, and state the restrictions on the variable : (x^2-x-6/x^2-4)/(x^2-2x+1/x^2-1)

a.) Essentially, you have one rational expression divided
by another. So let's simplify each one
individually:

(x^2-x-6)   =  (x-3)(x+2)  = 
(x-3)

(x^2-4)          (x-2)(x+2)     
(x+2)

In the second step, in its factored form, we find the
restrictions for the denominator are x cannot equal positive or negative
2.

Repeat for the second
expression:

(x^2-2x+1)  =  (x-2)(x+1)  = 
(x-2)

(x^2-1)            (x-1)(x+1)     
(x-1)

Our restrictions here: x cannot be positive or
negative 1.

Division is the same as multiplying by the
reciprocal. Now take the first simplified expression and multiply it by the reciprocal
of the second.

(x-3)
(x-1)

(x+2) (x-2)     with the given restrictions x is not
1, -1, 2, -2