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June 2, 2014
- 1. Today: Final ExamReview Rational Expressions Review Adding/Subtracting Rational Expressions Class Work Khan Academy Due Tomorrow for Everyone June 2, 2014
- 2. The specs forSamsung’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. Write the equationfor 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. Final Exam Review:(June 11th )
- 5. Simplifying Rational Expressions& Multiplying/Dividing Simplify; Excludify = (𝒃 −𝟒)(𝒃+𝟐) (𝒃+𝟓)(𝒃+𝟐)) = (𝒚 −𝟗)(𝒚+𝟐) (𝒚−𝟗))
- 6. −𝒙+𝟓 𝒙 𝟐−𝟏𝟐𝒙+𝟑𝟐 + 𝟐𝒙−𝟗 𝒙 𝟐−𝟏𝟐𝒙+𝟑𝟐 = −𝒙+𝟐𝒙+𝟓−𝟗 𝒙𝟐−𝟏𝟐𝒙+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. 𝟒𝒙 𝟑𝒙 𝟐−𝒙−𝟐 − 𝒙−𝟐 𝟑𝒙 𝟐−𝒙−𝟐 = 𝟒𝒙−(𝒙−𝟐) 𝟑𝒙𝟐−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. = 𝟏𝟏 𝟏𝟐 𝟑 𝟒 + 𝟏 𝟔 𝟏𝟐 𝟏𝟐 𝟏𝟐 𝟏𝟐 = 𝟑 𝟒 + 𝟏 𝟔 Adding and SubtractingRational 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. 𝟑 𝒙 + 𝟏 𝟔 = 𝟑∙𝟔 𝒙∙𝟔 + 𝟏∙𝒙 𝒙∙𝟔 LCD=6x = 𝟏𝟖+𝒙 𝟔𝒙 Adding and SubtractingRational Expressions with unlike Denominators
- 10. Adding and SubtractingRational 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. 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. 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. 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