Simplify the difference (a^2-a-2)/(a^2-7a+-2a-3)/(a^2+5a+4)

(a^2 - a - 2)/(a^2 - 7a + 10)  -  (a^2 - 2a -3)/(a^2 + 5a + 4)
Factor first.
(a - 2)(a + 1)              (a - 3)(a + 1)
    -       
(a - 2)(a - 5)              (a + 4)(a + 1)

Cancel the common factors in each term. The (a-2)'s in the first term and the (a + 1)'s in the second term.

(a + 1)        (a - 3)
  -   
(a - 5)        (a + 4)

Now get the LCD of the two terms: The product of (a - 5)(a + 4). Leave in this form. Multiply the first term by (a + 4) and the second term by (a - 5).

(a + 1)(a + 4) - [ (a - 3)(a - 5) ]      FOIL the binomials

             (a - 5)(a + 4)

a^2 + 5a + 4 - [a^2 - 8a + 15]  Distribute the negative through the [ ]

                 (a - 5)(a + 4)

a^2 + 5a + 4 - a^2 + 8a - 15        Combine like terms

                 (a - 5)(a + 4)

13a - 11

(a - 5)(a + 4)