Topics:
In case you prefer to view videos on any of these topics, Here is a copy of the Course Outline with links to video resources for each topic.
• Complex Fractions Method II
In this method, we simplify a complex fraction as follows:
First find the LCM of all the denominators in the top and bottom of the complex fraction
Then multiply the top and bottom of the complex fraction by the LCM – don’t forget to distribute!
Then cancel: each denominator in the top and bottom should now be eliminated. We call this “clearing the denominators”.
Then simplify more if necessary.
Make sure that you understand and can use both methods! Sometimes one is easier than the other, and you will learn how to know this by experience. It’s a good idea to use both methods in the beginning until you see how they work.
Here are some outline notes (you can fill in the computations) on both methods for simplifying complex fractions:
• Solving Fractional Equations (Rational Equations)
We solve these equations by using the LCM of all the denominators to clear the denominators by multiplying both sides by the LCM (and don’t forget to distribute!). You do not need to change to a common denominator, and you should not do so – it only makes solving harder.
Also, beware that sometimes you get “solutions” from this method which are not solutions of the original equation, because they lead to a 0 denominator when you substitute back in. Therefore it is necessary to check all solutions to see of they really are solutions, when solving a rational equation!
