1. Unit 7 Rationals and Radicals Rational Expressions –Reducing/Simplification –Arithmetic (multiplication and division) Radicals –Simplifying –Rational Exponents

2. Rational Expressions Definition:  Fractions that contain integers in their numerator and/or denominator are called rational numbers  Fractions that contain polynomials in their numerator and/or denominator are called rational expressions.  Reminder: The denominator can never be zero.

3. Simplifying Rational Expressions  Factor the numerator and denominator completely  Factor out the GCF FIRST  Count the number of terms  2 Terms: try difference of squares  3 Terms: try trinomial factoring  4 Terms: try factoring by grouping  Cancel out factors that are common to both the numerator and denominator

4. Simplifying Rational Expressions

6. Simplifying Rational Expressions Things NOT to do:

7. Multiplying Rational Expressions Our Plan of Attack  Factor all the numerators and denominators  Cancel out factors common to the numerators and denominators  Multiply the numerators  Multiply the denominators

8. Multiplying Rational Expressions

9. Dividing Rational Expressions Our Plan of Attack: Dividing rational expressions is very much like multiplying rational expressions with one extra step  KEEP – SWITCH - FLIP: Keep the first fraction, Switch to multiplication, Flip the second fraction upside down  Factor all the numerators and denominators  Cancel out factors common to the numerators and denominators  Multiply the numerators  Multiply the denominators

10. Dividing Rational Expressions

11. Radical Expressions where n is the INDEX of the radical. The index tells us what root we are taking! If there is no number for the index, it is understood to be a square root

12. Examples of Radicals

15. Rational Exponents

17. You try it:

18. Questions?