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Addition and Subtraction of Rational Expressions with Like Denominators

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Addition and Subtraction of Rational Expressions with Like Denominators

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Addition and Subtraction of Rational Expressions with Like Denominators

  1. 1. Grade 8 – Mathematics Quarter I ADDITION AND SUBTRACTION OF RATIONAL ALGEBRAIC EXPRESSIONS (LIKE DENOMINATORS)
  2. 2. 1. recall addition and subtraction of similar fractions; and 2. add and subtract rational algebraic expressions with like denominators.
  3. 3. How do we add and subtract similar fractions? 𝟐 𝟒 + 𝟏 𝟒 Similar Fractions 1. Add or subtract the numerator then copy the common denominator. 2. Simplify, if possible. = 𝟑 𝟒 𝟒 𝟔 - 𝟐 𝟔 = 𝟐 𝟔 = 𝟏 𝟑
  4. 4. How do we add and subtract similar fractions? 𝟑 𝟓 + 𝟏 𝟓 Similar Fractions 1. Add or subtract the numerator then copy the common denominator. 2. Simplify, if possible. = 𝟒 𝟓 𝟑 𝟔 - 𝟐 𝟔 = 𝟏 𝟔
  5. 5. ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH LIKE DENOMINATORS 1. Add or subtract the numerator. 2. Copy the common denominator. 3. Factor the numerator and cancel out or divide the common factor then simplify. 𝒂 𝒄 + 𝒃 𝒄 = 𝒂+𝒃 𝒄 𝒂 𝒄 - 𝒃 𝒄 = 𝒂−𝒃 𝒄 𝒄 ≠ 𝟎
  6. 6. ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH LIKE DENOMINATORS 𝟐𝒂 𝟒𝒃 + 𝟑 𝟒𝒃 Add the numerator = 𝟐𝒂 + 𝟑 𝟒𝒃 Copy the common denominator. Factor the numerator. Simplify.
  7. 7. ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH LIKE DENOMINATORS 𝟏𝟎𝒄 𝟏𝟑 + 𝟏𝟔𝒄 𝟏𝟑Add the numerator = 𝟐𝟔𝒄 𝟏𝟑 Copy the common denominator. Factor the numerator. = 𝟏𝟑(𝟐𝒄) 𝟏𝟑 Simplify. = 𝟐𝒄
  8. 8. ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH LIKE DENOMINATORS 𝟖𝒅−𝟑 𝟗 + 𝟒𝒅+𝟏𝟐 𝟗Add the numerator = 𝟖𝒅 − 𝟑 + 𝟒𝒅 + 𝟏𝟐 𝟗Copy the common denominator. Factor the numerator. Simplify. = 𝟏𝟐𝒅 + 𝟗 𝟗 = 𝟑(𝟒𝒅 + 𝟑) 𝟗 𝟑 𝟏 = 𝟒𝒅 + 𝟑 𝟑
  9. 9. ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH LIKE DENOMINATORS 𝟗𝒙 𝟐 𝟑𝒙−𝟓 - 𝟐𝟓 𝟑𝒙−𝟓 Subtract the numerator = 𝟗𝒙 𝟐 − 𝟐𝟓 𝟑𝒙 − 𝟓 Copy the common denominator. Factor. Simplify. 𝟗𝒙 𝟐 − (𝟐𝟓) = (𝟑𝒙 + 𝟓)(𝟑𝒙 − 𝟓) 𝟑𝒙 − 𝟓 = 𝟑𝒙 + 𝟓
  10. 10. ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH LIKE DENOMINATORS 𝟗𝒚 𝟐 𝒚−𝟐 - 𝒚 𝟐+𝟏𝟔𝒚 𝒚−𝟐 Subtract the numerator = 𝟗𝒚 𝟐 − 𝒚 𝟐 − 𝟏𝟔𝒚 𝒚 − 𝟐 Copy the common denominator. Factor. Simplify. 𝟗𝒚 𝟐 − (𝒚 𝟐 + 𝟏𝟔𝒚) = 8𝒚(𝒚 − 𝟐) 𝒚 − 𝟐 = 𝟖𝒚 = 𝟖𝒚 𝟐 − 𝟏𝟔𝒚 𝒚 − 𝟐
  11. 11. ADDING AND SUBTRACTING RATIONAL EXPRESSIONS WITH LIKE DENOMINATORS 𝒉 𝟐+𝟖𝒉−𝟏𝟓 𝟑𝒉 𝟐−𝟗𝒉 - 𝟒𝒉+𝟔 𝟑𝒉 𝟐−𝟗𝒉 Subtract the numerator = 𝒉 𝟐 + 𝟖𝒉 − 𝟏𝟓 − 𝟒𝒉 − 𝟔 𝟑𝒉 𝟐 − 𝟗𝒉Copy the common denominator. Factor. Simplify. = 𝒉 𝟐 + 𝟒𝒉 − 𝟐𝟏 𝟑𝒉 𝟐 − 𝟗𝒉 𝒉 𝟐 + 𝟖𝒉 − 𝟏𝟓 − (𝟒𝒉 + 𝟔) = (𝒉 + 𝟕)(𝒉 − 𝟑) 𝟑𝒉(𝒉 − 𝟑) = 𝒉 + 𝟕 𝟑𝒉

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