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Rational algebraic expressions
- 2. • It is a ratio of two polynomials with a denominator not equal to zero. • It is in the form 𝑎 𝑏 , where 𝑏 ≠ 0 What is a Rational Algebraic Expression?
- 3. 9 10 EXAMPLES OF RATIONAL EXPRESSIONS 7𝑥 2𝑦 40 + 𝑥 15 + 𝑥 10 − 𝑛 12 − 𝑛 2𝑐𝑑 + 𝑑 3𝑐2 + 5𝑐 − 𝑑 3𝑦 + 5 𝑦 + 1
- 4. 10𝑥−5 𝑥+3 Rational Expression is defined for all r eal numbers for which the denominato r is not equal to zero. This rational expression is defined for all real numbers except −3 since it will make the denominator 𝑥 + 3 equal to zero.
- 5. 7+𝑥 2𝑥 This rational expression is defined for all real numbers except 0 since the denominator 2 0 is equal to zero. 5 𝑥2−4 𝑥2 − 4 = 0 𝑥2 = 4 𝑥 = ± 4 𝑥 = ±2 The expression is defined for all real numbers except 2 and -2.
- 7. Factor both the numerator and denominator of the fraction and then cancel the common factors. How to simplify Rational Expressions? 18 24 = 6 ∙ 3 6 ∙ 4 = 3 4
- 8. 1. 𝒙 𝒙 = 𝟏 CANCELLATION LAWS 𝒂 − 𝒃 𝒂 − 𝒃 = 𝟏 𝒙 + 𝟓 𝒙 + 𝟓 = 𝟏 Example 1: Example 2:
- 9. 2. 𝑥𝑦 𝑥𝑧 = 𝑦 𝑧 CANCELLATION LAWS Example 1: 𝟐𝒙 𝟑𝒙 = 𝟐 𝟑 𝟐(𝒄 − 𝟑𝒅) 𝟐(𝒄 + 𝟑𝒅) = Example 2: 𝒄 − 𝟑𝒅 𝒄 + 𝟑𝒅
- 10. 3. 𝑥 𝑦 ∙ 𝑦 𝑧 = 𝑥 𝑧 CANCELLATION LAWS Example 1: 𝟐 𝒑 𝟐 ∙ 𝒑 𝟐 𝒑 − 𝟏 = 𝟐 𝒑 − 𝟏 𝒙 𝒙 + 𝟏 ∙ 𝒙 + 𝟏 𝟑𝒚 = 𝒙 𝟑𝒚 Example 2:
- 11. 4. 𝑥 𝑦 ∙ 𝑧 𝑥 = 𝑧 𝑦 CANCELLATION LAWS Example 1: 𝒓 𝒔 − 𝟐 ∙ 𝒔 − 𝟑 𝒓 = 𝒔 − 𝟑 𝒔 − 𝟐 𝒙 + 𝟑 𝒙 + 𝟐 ∙ 𝒙 𝒙 + 𝟑 = 𝒙 𝒙 + 𝟐 Example 2:
- 12. 5. 𝑥 ∙ 𝑦 𝑥 = 𝑦 CANCELLATION LAWS Example 1: 𝒉 ∙ 𝟐𝒈 𝒉 = 𝟐𝒈 (𝒉 − 𝟐) ∙ (𝒉 + 𝟐) (𝒉 − 𝟐) = 𝒉 + 𝟐 Example 2:
- 13. 6. 𝑥 𝑦 ∙ 𝑦 = 𝑥 CANCELLATION LAWS Example 1: 𝒌 − 𝟐 𝒋 − 𝟒 ∙ 𝒋 − 𝟒 = 𝒌 − 𝟐 (𝒚 + 𝟐) (𝒚 − 𝟐) ∙ 𝒚 − 𝟐 = 𝒚 + 𝟐 Example 2:
- 14. Examples when not to cancel terms. Example 1: 𝟐 + 𝒙 𝟐 + 𝟕𝒙 𝒙 + 𝟏𝟎 𝒙 Example 2: Example 3: 𝟐 + 𝒙 𝟐 − 𝒙 ∙ 𝟐 + 𝒙 Example 4: 𝟐𝒚 ∙ 𝟐𝒚 𝟑𝒙
- 15. THANK YOU!