6-1:Adding and Subtracting Rational Expressions Unit 6: Rational and Radical Equations

Recall: Multiplying and Dividing Rational Expressions. Example 1: You must first factor any polynomials so that they are using multiplication instead of addition and subtraction. Once you were multiplying everything, you could then cancel out everything that matches.

Now: Adding and Subtracting Rational Expressions. We still must factor everything that we have in the problem, but we are looking to make the denominators all the same. Recall: Basic Fractions To find the common denominator, you will multiply 5 and 8

Here, we are doing exactly the same thing, except that the denominators are expressions instead of integers. This is just like what we did on the last slide, and the common denominator is found exactly the same way  Multiply then together

If they are already using multiplication, it can make it easier, sometimes  `(although I find the last slide much easier) ! First, find the common denominator  variables are easy  take the largest exponent of each one every time Then use the regular common denominator of the numbers Multiples of each coefficient 15  15, 30, 45, 60, 75, 90,  18, 36, 54,72, 90 I also need x and y 2 So, the common denominator is 90xy 2. Example 2:

The question you should be asking yourself now is: what do I need to turn each denominator into the common denominator? For 15y 2  For 18xy 

Ex. You will do the same with subtraction. Example 3:

Ex. Some look very hard, but if you take your time, you can solve them. Example 4:

Example 5: