1. Sec. 9-4: Rational Expressions

2. 1.Rational Expressions: Expressions (NOT equations that involve FRACTIONS). We will be reducing these expressions NOT SOLVING…we will solve rational EQUATIONS later. *** Remember, when you are working with fractions, you can “CANCEL” when you are dividing. YOU CANNOT CANCEL THRU ADDITION & SUBTRACTION!

3. 2.The Process: a. Factor the numerator & denominator of the expression. b. You can cancel (divide out) ANY numerator with ANY denominator when you only have multiplication & division in a problem. c. Remember, do NOT cancel thru addition or subtraction—you can cancel FACTORS. Let’s look at some examples:

4. x 2 + 2x – 3 x 2 + 5x + 6 Factor numerator and denominator. (x - 1)(x + 3) (x + 2)(x + 3) *** Notice I did NOT cancel the x 2 nor the 3 & -6. Final answer: x – 1 x + 2

5. If you multiply an expression, again factor first and divide out what you can. x 2 + 6x 4 10 x 2 – 36 x(x + 6) 4 10 (x – 6)(x + 6) x 2 5 (x – 6) 2x or 2x 5(x – 6)5x - 30

6. ** If you are dividing fractions, remember, you multiply by the RECIPROCAL. x 2 – 9 ÷ 4x – 12 6 x x 2 – 9 x 6 4x – 12 (x + 3)(x - 3) x 6 4(x – 3) x(x + 3) 24