This week we worked on adding/subtracting rational expressions. Just like adding or subtracting regular fractions, we need to have a common denominator meaning whatever we multiply the denominator by we need to multiply the numerator by, and then after that simplifying the equation and doing whatever factoring is needed.
Example:
Step 1: The first step is to make sure everything is factored. In this example everything was already factored so that step is done. Next state the restrictions. I find it much easier to do it at the start so I don’t forget when I have completed the question. The restrictions is anything that would make the denominator =0.
Step 2: Now we are going to look at the denominator and see what is missing from either side. I can see they both have a (d-2), so I don’t need to do anything with that. But the right side is missing a (d-4) as the left side is missing (d+1). So what I need to do is multiply either numerator with the missing denominator.
Step 3: Next, I FOIL the top, making sure I don’t make any mistakes as that would really mess up the rest of the question. I usually do this step twice to make sure everything was done correctly, as it’s very easy to make mistakes on.
Step 4: Now simplify the numerator. Collect all the like terms.
Step 5: Now look at the numerator and see if it can be factored. In this case it can be and I used the box method.
Step 6: Now you put the factored form in the numerator and your question is done.
And that is all you do. Always remember to state your restrictions!