1. Warm Up

2. B UILDING, U NDERSTANDING AND S IMPLIFYING R ATIONAL E XPRESSIONS

3. KCAS High School Algebra Standard (A-APR.7) – (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. Rewrite rational expressions Arithmetic with Polynomials and Rational Expressions (A- APR) I can simplify a rational expression.

4. Start with a simple fraction like

5. Multiply both the numerator and denominator by the arbitrary number 5.

6. Let x represent the number 3. When x = 3, then 4 becomes x + 1 And 5 becomes x + 2 Why?

7. Now the fraction becomes WHY?

8. Use the distributive property and the multiplication of binomials to reveal : An Algebraic Rational Expression

9. You can now check yourself by replacing x with 3. What is the result?

10. You can now reverse this thinking process to simplify any algebraic rational expression.

11. Try the whole process with And multiply by Check your results and then work backwards to simply your algebraic rational expression.

12. and multiply by Try Check your results and then work backwards to simply your algebraic rational expression.

13. Try and multiply by Check your results and then work backwards to simply your algebraic rational expression.

14. Ready?

15. Simplify Each: 1. 2.