1. Adding and subtracting rational expressions
With unlike denominators

2. Example – Express the following as a single fraction in simplest form
We can only combine fractions if they have the same denominator
As we can see, they don’t have the same denominator. Let’s factor.
The LCD =
Multiply the fraction on the left by

3. Now, we should simplify our final answer. Factor the numerator
We can divide by the common factor
Final answer

4. Express as a single fraction in simplest terms
Note that the denominators are not the same. But we cannot factor here!
The LCD in this case then is
Multiply the fraction on the left by x-2 and the fraction on the right by x+1

5. Factor to see if we can simplify further
We cannot simplify further so this is our final answer

6. Grab a pencil and paper and try these on your own (for complete solutions, come to SGI)