How do we reduce Rational Expressions?

Do Now: How do we reduce fractions? Reduce these fractions:

€

24

6

€

18

9

€

0

5

What is a Rational Expression?

• A rational expression is a fraction in the form of P1/P2 where P1 and P2 are both polynomials and P2≠0.

• Examples:

€

5

7

€

x

6

€

3

x

€

11

x −2

€

a− 3

a2 − 7a−9

What happens if we divide by zero?

• If we divide by zero, then the expression is undefined.

• We CAN NOT divide by zero.• If we do divide by zero, mathematics,

logic, and the world will blow up!• We must constantly be aware of

situations that will result in a zero in the denominator in the fraction.

For what values of x are the following rational expressions

undefined?

€

5

x

€

x −2

x 2 −9

Try on your own

€

11

x − 7

€

x 2 − x −12

x 2 − 7x +10

How do we reduce Rational Expressions?

• The first thing we must do is FACTOR.– When you factor, make sure each term has a

positive x in the front.– Ex. 8–x will be factored –(x–8)

• Once we have something FACTORED, then we cancel out common terms.– The only terms we can cancel are those that are

multiplied

• Remember to state values of x for which the expression is undefined.

Express in simplest form

€

16x 4y 3z6

24x 3yz10

€

x 2 −25

5x − x 2

Try on your own

€

21a3bc 6

28a2b4c 6

€

6x +18

x 2 + x −6

€

24 −6x

x 2 − 7x +12

Summary/HW

• Why can’t we just cancel out the x in the following rational expression to get the stated result?

• HW: pg 116, 16-20

€

2x

x − 3=2

−3