Algebra: Chapter 10, Lesson 5, page 445.
Addition and Subtraction: Unlike Denominators (Chapter 10-5)
This lesson is TOUGH and takes time to do right. We have to bring all of our tools to the problem. Know how to FOIL, recognize binomial squares (the difference of 2 squares), and use the BOX method of FACTORING ACCURATELY.
Unlike Lesson 4, we have differing denominator terms and we must find a common denominator of both rational expressions.
Given that p, q, r and s are rational numbers or expressions, the easiest way for addition and subtraction is with this equation: `(p/q) + (r/s)` converts to become `(ps + rq)/(qs)` for addition or `(ps – rq)/(qs)` for subtraction. We are sort of criss-crossing like we did for ratios!
Sometimes, we need to find the LCM (least common multiple of the denominators. These steps will help:
- Factor each expression
- For the product using each factor the greatest number of times it occurs.
- Just go slow and be methodical.
SHOW ALL THE WORK and you’ll be fine, try shortcuts and you’ll regret it.
Purplemath has a good explanation and plenty of examples here too. Just make sure to scroll down to the middle of the page and the next page as well.