Algebra II Honors POD

homework: p. 55 7-31 eoo, 35-39 odds

Factor the following:

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a) 3x32 − 9x

12 + 6x

−12

b) 2 + x( )−23 x+ 2 + x( )

13

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a) 3 x -1( ) x − 2( )

x12

b) 2 1+ x( )

2 + x( )23

Simplifying Rational Expressions

1) Factor the numerator and denominator2) Reduce (cancel)

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x2 − 5x+ 6x2 − 4

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x − 3( ) x − 2( )x+ 2( ) x − 2( )

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x − 3( )x+ 2( )

Multiplying or Dividing Rational Expressions

1) Change any divisions to multiplication.(multiply by the reciprocal)

2) Factor all numerators and denominators.

3) Reduce up and down, or diagonally. (never side to side )

4) Write as one fraction.

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49

÷ 827

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49⋅27

8

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2 ⋅23⋅3

⋅ 3⋅3⋅32 ⋅2 ⋅2

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32

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x2 − 4x+ 412x+ 30

÷ x2 − 42x2 +13x+ 20

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x2 − 4x+ 412x+ 30

⋅ 2x2 +13x+ 20x2 − 4

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x − 2( ) x − 2( )6 2x+ 5( )

⋅ 2x+ 5( ) x+ 4( )x+ 2( ) x − 2( )

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x − 2( ) x+ 4( )6 x+ 2( )

Algebra II Honors Problem of the DayHomework: p. 56 41-65 eoo

Factor the following:

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a) x2 + 2x( )2

− 2 x2 + 2x( ) − 3

b) 13x+ 6( )−2

3 2x − 3( )2 + 2( ) x+ 6( )13 2( ) 2x − 3( )

Add and Subtract Rational Expressions

1) Factor the denominator of each term2) Find the LCD3) Rewrite each term with the appropriate LCD4) Add or subtract numerators5) Write the answer over the LCD

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xx2 − x − 6

− 1x+ 2

− 2x − 3

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xx+ 2( ) x − 3( )

− 1x+ 2

− 2x − 3

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xx+ 2( ) x − 3( )

− 1x+ 2( )

⋅ x − 3( )x − 3( )

− 2x − 3( )

⋅ x+ 2( )x+ 2( )

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xx+ 2( ) x − 3( )

+ −x+ 3x − 3( ) x+ 2( )

+ −2x − 4x − 3( ) x+ 2( )

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x − x+ 3− 2x − 4x+ 2( ) x − 3( )

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−2x −1x+ 2( ) x − 3( )

Simplifying Mixed Expressions

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2 + 59

3+ 59

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189

+ 59

279

+ 59€

239329

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239⋅ 932

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2332

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3+ xx+1

3− xx+1

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3 x+1( )x+1( )

+ xx+1

3 x+1( )x+1( )

− xx+1

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3x+ 3+ xx+1( )

3x+ 3− xx+1( )

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4x+ 3x+1( )

2x+ 3x+1( )

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4x+ 3x+1( )

⋅ x+1( )2x+ 3

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4x+ 32x+ 3

Using a Conjugate to Rationalize a Denominator

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2x − 5

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2x − 5

⋅x+ 5( )x+ 5( )

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2 x+ 5( )x2 − 5

Problem of the Day: Group work handout.

Homework: p. 56 67, 71-75 odds, 77-97 eoo