3.2.2 Notes Use 2018­19 finished.notebook November 06, 2018

     Today's Agenda: • any ?s on corrections

• Start 3.2.2 notes• YOTL....WS

Joke of the Day :        What plays music on your head?

a Head Band!

Today's TargetI Can...

...

3.2.2 Notes 

simplify rational expressions

and find the restrictions.

3.2.2 Notes Use 2018­19 finished.notebook November 06, 2018

Multiply or DivideName __________________________________  Period  ____

x2 + 10x + 25

x2 + 9x + 20

x2 - 9

3x - x2

x2 + 5x +4

2x2+7x+3

x2+8x+15

3.2.2  Rationals INTRO 

Factor:

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9.4 Rationals INTRO

3.2.2 - Rational Expressions

Rational Expression - a fraction where the numerator and denominator are polynomials

Examples:

a) 4 b) x2 - 25 c) x2 + 7x + 12 x + 1 x + 5 x2 - x - 12

I can: simplify rational expressions

and find the restrictions.

3.2.2 Notes Use 2018­19 finished.notebook November 06, 2018

To put a rational expression in simplest form means:

top and bottom will have no common factors

Examples of simplest form:

12 = (4)(3) = (4)(3) = 3 8 (4)(2) (4)(2) 2

a.

b. (x+2)(x+3) = (x+2)(x+3)= (x+3) x(x+2) x(x+2) x

                    

ex 1

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Common mistakes!!

c. 4 + 3 = 7 4 4

mistake:

4 + 3 = 3 4

OR

a. 5(5+6) = 5 4(5+6) 4

b. x5(x+3) = x2

x3(x+3)

c. x + 5 = x 5

d. (x+2)(x-4) = 2 x(x-4)

   

ex 2

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A denominator may not be

 the number,  _____.

Therefore you must state restrictions.  Restrictions are needed to prevent the denominator of the original expression from being 0.

"In your own words, ask, ____________________________________and use this notation:  _________________

Reduce the following:

x2 + 10x + 25 = x + 5x2 + 9x + 20 x + 4

x2 - 9 = x + 33x - x2 -x

Ex 3State restrictions on the variable.

Ex 4

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Ex. 5

*** Interesting!

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YOTL:    

WS 3.2.2

Today's TargetI Can...

...

9.4 Day 2

multiply and divide rational expressions and find the restrictions.

3.2.2 Notes Use 2018­19 finished.notebook November 06, 2018

DAY 2 Mult/Div Rationals

3.2.2 Notes Use 2018­19 finished.notebook November 06, 2018

Additional Things to Watch!  :

   a         ­a    a­       =    =     b  b   ­b

  a     c   =  ac  b     d       bd

  a         a    d         ad  b    =   b    c   =    bc    c  d

  m   =    m    =  m   q  =   p          1         1     p    q          p               q

(5­x)  =  (­x+5)  = ­(x­5)

Put in simplest form:

x2 + 5x +4    x2 ­ 1    x + 5

ex 1

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a.  2x2+7x+3          x2­16         x ­ 4           x2+8x+15

    

ex 2 Multiply.  State any restrictions.

      4­x                    5(x­4)  (3x+2)(x­2)       (x­2)(7y­5)

ex. 3

÷

 Divide. State any restrictions.

3.2.2 Notes Use 2018­19 finished.notebook November 06, 2018

      2x2 ­ 6x             x2 ­ 9      x2 +18x +81        9x + 81

ex. 4

÷

Divide. State any restrictions.

        YOTL: 

  WS 9­4AND TEST INTERVENTION to BUY A BONUS QUIZ

3.2.2 Notes Use 2018­19 finished.notebook November 06, 2018

        YOTL: 

  p. 511, 512    7 ­ 17, odd,  27 ­ 31 odd, check your answers in back of book for accuracy