Step by step breakdown

Whenever you have expressions in your fractions, you want to see if you can factor anything. The numerator (x-2) is already in simpliest form, so let's look at the denominator (8x^{2}-32). I see a common factor of 8, so let's pull that out. You get
8(x^{2}-4). But, we're not done! Did you recognize that difference of squares? Let's factor again: 8(x-2)(x+2).

Let's put it all together. The (x-2) in the numerator cancels with the (x-2) in the denominator. The final answer is 1/8(x+2).