Adding and subtracting rational expressions

Finding the LCM, Addition and Subtraction of Rational Expressions

1. Using fraction rules learned in elementary school, we will add and subtract rational expressions. Adding and Subtracting Rational Expressions

2. The Basics! Let’s remind ourselves how we add and subtract fractions.   And when the denominators are different…  

3. Finding Common Denominators Our Common Denominator will be the LCM of the denominators. We will list the factors of each. Each factor must be represented in the LCM.     LCM will have:  

4. Practice find LCMs We will do the same with polynomials. LCM will have:    

5. Practice find LCMs We will do the same with more complicated polynomials. LCM will have:     With polynomials in this form, we will leave in factored form and not multiply the polynomials out into standard form.

6. Adding Rational Expressions   Common Denominators already!

7. Adding Rational Expressions   Need Common Denominators!   LCM will be:    

8. Subtracting Rational Expressions   Need Common Denominators!   LCM will be:    

9. Complete the given operation   Neither of the denominators can be factored, so our LCM =    

10. Special Cases to watch out for!   Our first fraction has an understood denominator of 1, so our LCM =    

11. Another Special Case!   Our denominators are similar but not equal…YET!     So our LCM =