First, factor the expression on the top. What two numbers add to get 8 and multiply to 15? 5 and 3! so the top expression factors to (x+3)(x+5). You can cancel the x+3 from the denominator and end up with x+5. Make sense?
take the x and drop it down after that the - needs to become the postive with takes multiple and so then after tyat it needs to add the extra 1 bc if the 1