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Section 1.4 Rational Expressions

Chapter 1 - Fundamentals. Section 1.4 Rational Expressions. Definitions. Fractional Expression A quotient of two algebraic expressions is called a fractional expression. Rational Expression

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Section 1.4 Rational Expressions

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  1. Chapter 1 - Fundamentals Section 1.4 Rational Expressions 1.4 - Rational Expressions

  2. Definitions • Fractional Expression A quotient of two algebraic expressions is called a fractional expression. • Rational Expression A rational expression is a fractional expression where both the numerator and denominator are polynomials. 1.4 - Rational Expressions

  3. Domain The domain of an algebraic expression is the set of real numbers that the variable is permitted to have. 1.4 - Rational Expressions

  4. Basic Expressions & Their Domains 1.4 - Rational Expressions

  5. Simplifying Rational Expressions To simplify rational expressions we must • Factor the numerator and denominator completely. • State the restrictions or domain. • Reduce the common factors from the numerator and denominator. 1.4 - Rational Expressions

  6. Example 1 • Simplify the following expression. 1.4 - Rational Expressions

  7. Multiplying Rational Expressions To multiply rational expressions we must • Factor the numerator and denominator completely. • State the restrictions or domain. • Multiple factors. • Reduce the common factors from the numerator and denominator. 1.4 - Rational Expressions

  8. Example 2 • Perform the multiplication and simplify. 1.4 - Rational Expressions

  9. Dividing Rational Expressions To divide rational expressions we must • Factor the numerator and denominator completely. • State the restrictions or domain. • Invert the divisor and multiply. • State new restrictions. • Reduce the common factors from the numerator and denominator. 1.4 - Rational Expressions

  10. Example 3 – pg. 42 #33 • Perform the multiplication and simplify 1.4 - Rational Expressions

  11. Adding or Subtracting Rational Expressions To add or subtract rational expressions we must • Factor the numerator and denominator completely. • State the restrictions or domain. • Find the LCD. • Combine fractions using the LCD. • Use the distributive property in the numerator and combine like terms. • If possible, factor the numerator and reduce common terms. 1.4 - Rational Expressions

  12. Example 4 – pg. 42 #48 Perform the addition or subtraction and simplify. 1.4 - Rational Expressions

  13. Compound Fractions • A compound fraction is a fraction in which the numerator, denominator, or both, are themselves fractional expressions. 1.4 - Rational Expressions

  14. Simplifying Compound Fractions To simplify compound expressions we must • Factor the numerator and denominator completely. • State the restrictions or domain. • Find the LCD. • Multiply the numerator and denominator by the LCD to obtain a fraction. • Simplify. • If possible, factor. 1.4 - Rational Expressions

  15. Example 5 – pg. 42 #60 Perform the addition or subtraction and simplify. 1.4 - Rational Expressions

  16. Rationalizing • If a fraction has a numerator (or denominator) in the form then we may rationalize the numerator (or denominator) by multiplyting both the numerator and denominator by the conjugate radical . 1.4 - Rational Expressions

  17. Example 6 – pg. 43 #81 • Rationalize the denominator. 1.4 - Rational Expressions

  18. Example 7 – pg. 43 #87 • Rationalize the numerator. 1.4 - Rational Expressions

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