1. 9.3 Simplifying and Multiplying Rational Expressions
4/13/2014

2. Rational Expression:
an expression that is the ratio of two polynomials.
It is "Rational" because one is divided by the other, like a ratio.
the polynomial you are dividing by cannot be zero.
Note:
Ex:

3. Simplify the rational expression, if possible.
Example 1
Simplify a Rational Expression
Simplify the rational expression, if possible.
15x = • x 5
Divide out the common factor
5 and simplify. a.
=3𝑥 5 b. x
x 5 +
This expression is already in simplest form. c.
14x2 6x
x x = • x
Divide out the common factors 2 and x.
= 3 7𝑥 3

4. Simplify the expression, if possible.
Checkpoint
Simplify a Rational Expression
Simplify the expression, if possible. 4x
ANSWER 2x 5 1. 10 2. 8 4x
ANSWER 2 x 9x ( 12 1 x + 3.
ANSWER 3x ( 4 1 x + x 1 – 4.
ANSWER
already in simplest form

5. Simplify the expression, if possible.
Checkpoint
Write in Simplest Form
Simplify the expression, if possible. 2x 1 + 5.
ANSWER
already in simplest form 6. 3x ( ) 1 x +
3x 2
ANSWER x ( ) 1 +

6. Simplify the expression, if possible.
Checkpoint
Write in Simplest Form
Simplify the expression, if possible.
2x 2 + 8x 7.
12x
ANSWER 6 4 x + 8. 2 x + 6 3x
ANSWER 3 1

7. Multiply . Simplify the result. • 3x 8x 5
Example 3
Multiply Rational Expressions
4x 2 9x
Multiply Simplify the result. • 3x
8x 5
SOLUTION 3x
4x 2 9x •
8x 5 1 3 1 2
= 3 𝑥 2 2 𝑥 5
Subtract exponents of x =
2x 3 3 7

8. Multiply . Simplify the result. • x x 2 9 – 4x 3x 12
Example 4
Multiply Rational Expressions
Multiply Simplify the result. • x
x 2 9 – 4x 3x 12
SOLUTION • x
x 2 9 – 4x 3x 12
Factor the numerators and
denominators. = 4 3x ( ) 3 x – + • = 4 ( ) 3 x + 8

9. Multiply the rational expressions. Simplify the result.
Checkpoint
Multiply Rational Expressions
Multiply the rational expressions. Simplify the result. 9. 14 3x 7x •
6x 3
ANSWER 4x 1 •
x 2 2x 4 – 3x 6
10.
ANSWER 3x 4 •
x 2 6x 4 –
11. 4x 8 +
x 3
ANSWER 24
x 2 ( ) 2 x –

10. Multiply . Simplify the result. • 3 ( 2 – x (
Example 5
Multiply by a Polynomial x
x 2 – 6 5x +
Multiply Simplify the result. • 3 ( 2 – x (
SOLUTION • x
x 2 + 5x 6 ( 2 – 3
Write polynomial as a
rational expression. = • 1 x
x 2 + 5x 6 ( 2 – 3
Factor out of 1 – (
2 x = • x 2 3
Simplify. = x – 3x 3 10

11. Multiply the expressions. Simplify the result.
Checkpoint
Multiply by a Polynomial
Multiply the expressions. Simplify the result. x + 4
12. 2x ( • 3 6
ANSWER 8 x
13. 3x +
x 2 ( • 12 4x
ANSWER
x 2 3 3x
14.
x 2 • – ( 2 x
ANSWER x 3x – + 1

12. Homework: 9.3 p.483 #22-52 even only
I’m reading a book about anti-gravity. I can’t put it down!!!