3x^2 - 7x+ 2/x^2+ 6x -16 * x+8/4x-8

You should have typed

(3x^2- 7x+ 2)/(x^2+ 6x -16) * (x+8)/(4x-8)

because without those parentheses only the
two terms next to the " / " are indicated as
divided.  To type a fraction all on one line
you must use parentheses around both numerators
and denominators.  Parentheses aren't necessary 
when you type them on two lines 
like this, though:

 3x²-7x+2      x+8
---------- · ------
 x²+6x-16     4x-8

Factor every numerator and denominator that
can be factored 

 (3x-1)(x-2)     x+8
------------ · --------
 (x+8)(x-2)     4(x-2)

Indicate the multiplication of all the
factors in the numerators as well as
in the denominator.  You must enclose
the x+8 in paretheses:

(3x-1)(x-2)(x+8)
-----------------
(x+8)(x-2)4(x-2)

Cancel one of the (x-2)'s in the bottom into
the (x-2) in the top and cancel the (x+8)'s.

        1    1    
(3x-1)(x-2)(x+8)
-----------------
(x+8)(x-2)4(x-2)
  1    1

(3x-1)
------
4(x-2)

Take the parentheses off the top, since
they aren't necessary when typed on
two lines:

 3x-1
------
4(x-2)

And if you like you can distribute on the
bottom to remove the parentheses there,
but it isn't required:

 3x-1
------
 4x-8

Edwin