Sec. 9-4: Rational Expressions

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!

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:

x2 + 2x – 3

x2 + 5x + 6

Factor numerator and denominator.

(x - 1)(x + 3)

(x + 2)(x + 3)

*** Notice I did NOT cancel the x2 nor the 3 & -6.

Final answer: x – 1

x + 2

If you multiply an expression, again factor first and divide out what you can.

x2 + 6x • 4 10 x2 – 36

x(x + 6) • 4 10 (x – 6)(x + 6)

x • 25 (x – 6) 2x or 2x

5(x – 6) 5x - 30

** If you are dividing fractions, remember, you multiply by the RECIPROCAL.

x2 – 9 ÷ 4x – 126 x

x2 – 9 • x 6 4x – 12

(x + 3)(x - 3) • x 6 4(x – 3)

x(x + 3) 24