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**Section 1.4 Rational Expressions**

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

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**1.4 - Rational Expressions**

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

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**1.4 - Rational Expressions**

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

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**Basic Expressions & Their Domains**

Domain (Set Notation) Domain (Interval Notation) 1.4 - Rational Expressions

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**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

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**1.4 - Rational Expressions**

Example 1 Simplify the following expression. 1.4 - Rational Expressions

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**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

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**1.4 - Rational Expressions**

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

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**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

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**1.4 - Rational Expressions**

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

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**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

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**1.4 - Rational Expressions**

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

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**1.4 - Rational Expressions**

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

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**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

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**1.4 - Rational Expressions**

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

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**1.4 - Rational Expressions**

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

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**1.4 - Rational Expressions**

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

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**1.4 - Rational Expressions**

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

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