9.3 Simplifying and Multiplying

Rational Expressions

4/26/2013

Example 1 Simplify a Rational Expression

Simplify the rational expression, if possible.

a.5

15x

c.14x26x

= • •3 5 x5

3x= Divide out the common factor 5 and simplify.

b.x

x 5+ This expression is already in simplest form.

2 7 x x= • •2 3 x• • • = 7x

3 Divide out the common factors 2 and x.

Checkpoint Simplify a Rational Expression

9x(12 1x

(+3.

xx1 –4.

ANSWER 3x(4 1x

(+

ANSWER already in simplest form

1.

Simplify the expression, if possible.

4x10

ANSWER 2x5

ANSWER 2x2. 8

4x

Checkpoint

Simplify the expression, if possible.

Write in Simplest Form

5.2x

12x +

ANSWER already in simplest form

6.3x

( )1x +3x 2

ANSWER x ( )1x +

Checkpoint Write in Simplest Form

Simplify the expression, if possible.

7.12x

8x2x 2 +

ANSWER6

4x +

8. 2x +63x +

ANSWER31

Example 3 Multiply Rational Expressions

Multiply . Simplify the result. 3x4x 2 9x

•8x 5

SOLUTION3x4x 2 9x

•8x 5

=2x 3

3

1

21

3

¿3 𝑥2

2𝑥5Subtract exponents of x

Example 4 Multiply Rational Expressions

Multiply . Simplify the result. •x

x 2 9–4x

3x12–

SOLUTION

•x

x 2 9–4x

3x12–

=4

( )3x +3

Factor the numerators anddenominators.

=4

3x( )3x – x

( )3x – ( )3x +•

Checkpoint

Multiply the rational expressions. Simplify the result.

Multiply Rational Expressions

9.143x 7x

•6x 3

ANSWER4x1

•x 2

2x 4–3x

2x6–

10. ANSWER3x4

•x 2

6x

4–11. 4x 8+

x 3ANSWER 24

x 2 ( )2x –

Example 5 Multiply by a Polynomial

Multiply . Simplify the result.(2 –(3•xx 2 – 65x +

x

Factor out of . 1– (2 x–(= •x

(x –( (x –(2 3 1•1– (x –(3 2

SOLUTION •x

x 2 +5x 6

(2 –(3 x–

Write polynomial as a rational expression.= •

1x

x 2 +5x 6(2 –(3 x

–

Simplify.=x –

3x–3

Checkpoint Multiply by a Polynomial

ANSWER 8

ANSWER x 2

3

Multiply the expressions. Simplify the result.

x +412. 2x (( +•

36

x13. 3x +x 2 (( +•12

4x

3x14. x 2 •– –

(2 –(x 2

x ANSWERx3x–+ 1

Homework:

9.3 p.483 #22-52 even only

I’m reading a book about anti-gravity. I can’t put it down!!!