SOLUTION: [(x^2-4)/(x^2+3x-10)] / [(x^2+5x+6)/(x^2+8x+5)]

Write it this way:

   x² - 4       x² + 5x + 6
------------ ÷ -------------
x² + 3x - 10    x² + 8x + 5

Invert the second fraction and change ÷ to ·


   x² - 4       x² + 8x + 5
------------ · -------------
x² + 3x - 10    x² + 5x + 6

Everything factors except the x² + 8x + 5.  
Are you sure that + 5 shouldn't have been a
+ 15?

 (x - 2)(x + 2)       x² + 8x + 5
---------------- · ----------------
 (x - 2)(x + 5)     (x + 3)(x + 2)

Indicate the multiplication of numerators
and denominators, all as one fraction:

 (x - 2)(x + 2)(x² + 8x + 5)
------------------------------
 (x - 2)(x + 5)(x + 3)(x + 2)

Cancel the (x - 2)'s

    1      
 (x - 2)(x + 2)(x² + 8x + 5)
------------------------------
 (x - 2)(x + 5)(x + 3)(x + 2)
    1
and cancel the (x + 2)'s

    1      1
 (x - 2)(x + 2)(x² + 8x + 5)
------------------------------
 (x - 2)(x + 5)(x + 3)(x + 2)
    1                    1

  x² + 8x + 5
----------------
 (x + 5)(x + 3)

If that 5 on top had been a 15 the top 
would have factored exactly like the 
bottom and then everything would have 
canceled out and given the answer 1.

But as it is, nothing else will cancel
and so you leave the answer just as it
is. 

Edwin