Your LCD is correct, but there is no need to expand it at this point.

The LCD will be the product of all the different factors in the denominator using their largest exponent if they have one.

In your case, you have two different denominators:2andx-2.

The LCD is their product:2(x-2).

You didn't say what answer you got, so I don't know where you might have gone wrong in your solution attempt.

Multiply each term by your LCD.

. Therefore is the only solution.