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# June 2, 2014

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### June 2, 2014

1. 1. Today:  Final Exam Review  Rational Expressions Review  Adding/Subtracting Rational Expressions  Class Work  Khan Academy Due Tomorrow for Everyone June 2, 2014
2. 2. The specs for Samsung’s latest, yet to be released phone, were leaked online Saturday. Based on the specs, what will the screen size be? 1” = 25 mm. 8.57”≈ 8 𝟏 𝟐 ” in. Final Exam Review: (June 11th )
3. 3. Write the equation for and graph the line perpendicular to the line shown and passing through the points (0,1) and (-2,0) Final Exam Review: (June 11th )
4. 4. Final Exam Review: (June 11th )
5. 5. Simplifying Rational Expressions & Multiplying/Dividing Simplify; Excludify = (𝒃 −𝟒)(𝒃+𝟐) (𝒃+𝟓)(𝒃+𝟐)) = (𝒚 −𝟗)(𝒚+𝟐) (𝒚−𝟗))
6. 6. −𝒙+𝟓 𝒙 𝟐−𝟏𝟐𝒙+𝟑𝟐 + 𝟐𝒙−𝟗 𝒙 𝟐−𝟏𝟐𝒙+𝟑𝟐 = −𝒙+𝟐𝒙+𝟓−𝟗 𝒙 𝟐−𝟏𝟐𝒙+𝟑𝟐 = 𝟏 𝒙−𝟖 = 𝒙−𝟒 𝒙 𝟐−𝟏𝟐𝒙+𝟑𝟐 = 𝒙−𝟒 (𝒙−𝟒)(𝒙−𝟖) Adding and Subtracting Rational Expressions with like Denominators
7. 7. 𝟒𝒙 𝟑𝒙 𝟐−𝒙−𝟐 − 𝒙−𝟐 𝟑𝒙 𝟐−𝒙−𝟐 = 𝟒𝒙−(𝒙−𝟐) 𝟑𝒙 𝟐−𝒙−𝟐 = 𝟒𝒙−𝒙+𝟐 𝟑𝒙 𝟐−𝒙−𝟐 = 𝟑𝒙+𝟐 𝟑𝒙 𝟐−𝒙−𝟐 = 𝟑𝒙+𝟐 (𝟑𝒙+𝟐)(𝒙−𝟏) = 𝟏 𝒙−𝟏 Adding and Subtracting Rational Expressions with like Denominators
8. 8. = 𝟏𝟏 𝟏𝟐 𝟑 𝟒 + 𝟏 𝟔 𝟏𝟐 𝟏𝟐 𝟏𝟐 𝟏𝟐 = 𝟑 𝟒 + 𝟏 𝟔 Adding and Subtracting Rational Expressions with unlike Denominators = 𝟗 𝟏𝟐 + 𝟐 𝟏𝟐 The LCD is the product of each unique (different) factor 4 = 2•2 6 = 2•3 1. Find the LCD of the denominators The LCD is 12 2. Multiply each fraction (top & bottom) by the LCD. 𝟑 𝟐
9. 9. 𝟑 𝒙 + 𝟏 𝟔 = 𝟑∙𝟔 𝒙∙𝟔 + 𝟏∙𝒙 𝒙∙𝟔 LCD=6x = 𝟏𝟖+𝒙 𝟔𝒙 Adding and Subtracting Rational Expressions with unlike Denominators
10. 10. Adding and Subtracting Rational Expressions with unlike Denominators The LCD of 5x and 𝑥2 is 5𝑥2  9 5𝑥 − 2 𝑥2 9 5𝑥 ∙ 𝒙 𝒙 − 2 𝑥2 ∙ 𝟓 𝟓 = 9𝑥 5𝑥2 − 10 5𝑥2 = 9𝑥−10 5𝑥2 1. Find the LCD of the denominators 2. Multiply each fraction by the remaining factors of the LCD 3. Perform the addition or subtraction
11. 11. Find the LCD = 6x2 = 10m5 = 12y4 = 4x6 3y3 4y4 10m2 5m5 4x6 2x6 3x2 2x2 Adding and Subtracting Rational Expressions with unlike Denominators t + 4 4t + 16 4t + 16 2r - 1 r + 4 (2r – 1)(r + 4)
12. 12. Find the LCD, Then solve: = 𝟑𝟏 𝟔𝒙 𝟐 LCD= 6𝒙 𝟐 LCD = 12y4 (4y)7 (3)5 (4y)3y3 (3)4y4 = 28y 15 12y4 12y4 = 𝟐𝟖𝒚−𝟏𝟓 𝟏𝟐𝒚 𝟒 +4 27 6x2 6x2 2 9 3x2 2x2 + (2)2 (3)9 (2)3x2 (3)2x2= + 7 5 3y3 4y4 Adding and Subtracting Rational Expressions with unlike Denominators
13. 13. Simplify: 𝟒 𝒚 + 𝟓 + 𝟔 𝒚 − 𝟐 = 𝟒 𝒚 + 𝟓 ∙ 𝒚 − 𝟐 𝒚 − 𝟐 + 𝟔 𝒚 − 𝟐 ∙ (𝒚 + 𝟓) (𝒚 + 𝟓) LCD= 𝒚 + 𝟓 𝒚 − 𝟐 𝟒(𝒚 − 𝟐) (𝒚 + 𝟓)(𝒚 − 𝟐) + 𝟔(𝒚 + 𝟓) (𝒚 + 𝟓)(𝒚 − 𝟐) = 𝟒𝒚 − 𝟖 (𝒚 + 𝟓)(𝒚 − 𝟐) + 𝟔𝒚 + 𝟑𝟎 (𝒚 + 𝟓)(𝒚 − 𝟐) = 𝟒𝒚 − 𝟖 + 𝟔𝒚 + 𝟑𝟎 (𝒚 + 𝟓)(𝒚 − 𝟐) = 𝟏𝟎𝒚 + 𝟐𝟐 ( 𝒚 + 𝟓)(𝒚 − 𝟐) Adding and Subtracting Rational Expressions with unlike Denominators