This week in math we learned how to add rational expressions with monomial denominators. I chose this topic because I like how it encorporates everything I have learned about fractions so far in math, and combines it with my understanding of factoring. This skill is important because as questions become harder, having the foundations of factoring, and evaluating fractions is extremely important and useful.
Lets look at some examples…
Example a.
Step 1. Are the denominators the same? Yes! we are lucky because there is no need to find a LCM.
Step 2. Is our denominator factorable? Yes! We always want to see if we can factor our denominator when adding a rational expression.
Step 3. Add 3h-8h above our factored denominator.
*Side note* Use the factored denominator to find our non permissable values; h cannot be 1 and h cannot be -4.
Example b.
Step 1. Are the denominators the same? No! This means you need to find the LCM.
Step 2. Find LCM; our LCM needs to include all parts of both of our denominators.
Step 3. Remeber… what you do on the bottom you must do to the top.
Step 4. You can go ahead and add together your numerators and put them over your LCM.
Glossary :
LCM: The least common multiple of two numbers is the smallest number that is a multiple of both of them.