It's just the old rule you learned in 4th or 5th grade:

"To divide by a fraction, invert and multiply"
 
  7      x-2 
----- ÷ -----
 x+2     14

Invert the second fraction and multiply

  7      14          98          98
----- × ----- = ------------ = ------
 x+2     x-2     (x+2)(x-2)     x²-4

But you weren't asked to divide it, you were only
asked what you would multiply by in order to
divide it, and that answer was the fraction to
be divided by inverted:

        14
       ----- 
        x-2

Edwin