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Multiplying & dividing rational algebraic expressions
- 1. MULTIPLYING & DIVIDING RATIONAL ALGEBRAIC EXPRESSIONS MODULE 7
- 2. HOW TO MULTIPLY RATIONAL EXPRESSIONS?
- 3. • Operations like multiplication and division are very common in fractions. • These operations can also be performed to rational expressions.
- 4. • To obtain the product of two or more rational expressions, we get the product of the numerators as well as the product of the denominators of the given expressions.
- 5. • Rational expressions are multiplied in a similar manner as multiplying rational numbers. • The rational expressions must be factored first before multiplying them so that common factors can be cancelled.
- 6. Multiply & simplify: EXAMPLE 1. 𝟐𝒙𝒚 𝟐 𝟑𝒛 𝟑 ∙ 𝟏𝟓𝒛 𝟓 𝟒𝒙 𝟐 𝒚 = 𝟐 ∙ 𝟑 ∙ 𝟓 ∙ 𝒙 ∙ 𝒚 ∙ 𝒚 ∙ 𝒛 ∙ 𝒛 ∙ 𝒛 ∙ 𝒛 ∙ 𝒛 𝟑 ∙ 𝟐 ∙ 𝟐 ∙ 𝒙 ∙ 𝒙 ∙ 𝒚 ∙ 𝒛 ∙ 𝒛 ∙ 𝒛 = 𝟓𝒚𝒛 𝟐 𝟐𝒙
- 7. Multiply & simplify: EXAMPLE 2. 𝒙 𝒙−𝟏 ∙ 𝒙−𝟏 𝟐 𝟑𝒙 𝟐 ∙ 𝟗 𝒙 𝟐−𝒙 = 𝒙 ∙ 𝒙 − 𝟏 𝒙 − 𝟏 ∙ 𝟑 ∙ 𝟑 𝒙 − 𝟏 ∙ 𝟑 ∙ 𝒙 ∙ 𝒙 ∙ 𝒙 𝒙 − 𝟏 = 𝟑 𝒙 𝟐
- 8. Multiply & simplify: EXAMPLE 3. 𝒂 𝟐 𝒃−𝟐𝒂𝒃 𝟐 𝒂 𝟐−𝟒𝒂𝒃+𝟒𝒃 𝟐 ∙ 𝒂 𝟐−𝟒𝒃 𝟐 𝒂𝒃 = 𝒂𝒃 𝒂 − 𝟐𝒃 ∙ 𝒂 + 𝟐𝒃 𝒂 − 𝟐𝒃 𝒂 − 𝟐𝒃 𝒂 − 𝟐𝒃 ∙ 𝒂𝒃 = 𝒂 + 𝟐𝒃 𝟏 = 𝒂 + 𝟐𝒃
- 9. HOW TO DIVIDE RATIONAL EXPRESSIONS?
- 10. • In dividing rational expressions, we multiply the numerator by the reciprocal of the denominator. • 𝐴 𝐵 ÷ 𝐶 𝐷 = 𝐴 𝐵 ∙ 𝐷 𝐶 = 𝐴𝐷 𝐵𝐶
- 11. Divide & simplify: EXAMPLE 1. 𝒙 𝟐+𝟐𝒙−𝟖 𝒙 𝟐+𝟒𝒙+𝟑 ÷ 𝒙−𝟐 𝟑𝒙+𝟑 = 𝒙 𝟐 + 𝟐𝒙 − 𝟖 𝒙 𝟐 + 𝟒𝒙 + 𝟑 ∙ 𝟑𝒙 + 𝟑 𝒙 − 𝟐 = 𝒙 + 𝟒 𝒙 − 𝟐 ∙ 𝟑 𝒙 + 𝟏 𝒙 + 𝟏 𝒙 + 𝟑 ∙ (𝒙 − 𝟐) = 𝟑 𝒙 + 𝟒 𝒙 + 𝟑 𝒐𝒓 𝟑𝒙 + 𝟏𝟐 𝒙 + 𝟑
- 12. Divide & simplify: EXAMPLE 2. 𝒙 𝟐−𝟔𝒙+𝟗 𝟒𝒙−𝟏𝟐 ÷ 𝒙 − 𝟑 = 𝒙 𝟐 − 𝟔𝒙 + 𝟗 𝟒𝒙 − 𝟏𝟐 ∙ 𝟏 𝒙 − 𝟑 = 𝒙 − 𝟑 𝒙 − 𝟑 ∙ 𝟏 𝟒 𝒙 − 𝟑 ∙ (𝒙 − 𝟑) = 𝟏 𝟒
- 13. Divide & simplify: EXAMPLE 3. 𝒙 𝟐 − 𝟑𝒙 − 𝟏𝟎 ÷ 𝒙 𝟐+𝟑𝒙−𝟏𝟎 𝒙 𝟐−𝟐𝟓 = 𝒙 𝟐−𝟑𝒙−𝟏𝟎 𝟏 ∙ 𝒙 𝟐−𝟐𝟓 𝒙 𝟐+𝟑𝒙−𝟏𝟎 = 𝒙+𝟐 𝒙−𝟓 ∙ 𝒙+𝟓 𝒙−𝟓 𝟏∙ 𝒙−𝟐 𝒙+𝟓 = 𝒙+𝟐 𝒙−𝟓 𝒙−𝟓 𝟏∙ 𝒙−𝟐 = 𝒙+𝟐 𝒙−𝟓 𝟐 𝒙−𝟐
- 14. THANK YOU