3. Simplify

This is a compound fraction. There are two methods which are commonly used for simplifying these expressions. The first is to do the addition or subtraction on the top or bottom in order to get single fractions on both top and bottom.

In order to add or subtract fractions, we need to find common denominators. The common denominator will be   x   on both the top and bottom.

Now that we have common denominators, we can add the fractions.

The top of the top is a quadratic trinomial which can be factored.

The reason for factoring at this point is that we can cancel at this point. Cancel the factors that would cancel if you inverted and multiplied.

and the answer is

x + 3

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