Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions The quotient of two polynomials is called a Rational Expression. Determining the Domain: Remember, the denominator cannot be zero (that would make the fraction undefined.) So a rational expression would have a domain of all real numbers, with the exception of values that make the denominator zero. Example: Find the domain of each of the following expressions 1. 2. 3.

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions The quotient of two polynomials is called a Rational Expression. Determining the Domain: Remember, the denominator cannot be zero (that would make the fraction undefined.) So a rational expression would have a domain of all real numbers, with the exception of values that make the denominator zero. Example: Find the domain of each of the following expressions 1. all real numbers except -4 2. All real numbers except -2, 3 3. All real numbers except -3, -7/2

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Rational Expressions. Write each numerator and denominator in terms of its factors, then simplify. Example: Write each expression in lowest terms. 1. 2. 3.

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Rational Expressions. Write each numerator and denominator in terms of its factors, then simplify. Example: Write each expression in lowest terms. 1. 1/5 2. 1 2m + 6 3. r + 1 r + 3

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Rational Expressions involving Multiplication. Write each numerator and denominator in terms of its factors, cancel out common factors, and simplify. Example: Find each product. 1. 2. 3.

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Rational Expressions involving Multiplication. Write each numerator and denominator in terms of its factors, cancel out common factors, and simplify. Example: Find each product. 1. 2a + 8 2. c + 4 c - 4 3. x 4

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Rational Expressions involving Division. First, change division to multiplication by finding the reciprocal of the second rational expression; then, write each numerator and denominator in terms of its factors, cancel out common factors, and simplify. Example: Find each product. 1. 2. 3.

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Rational Expressions involving Division. First, change division to multiplication by finding the reciprocal of the second rational expression; then, write each numerator and denominator in terms of its factors, cancel out common factors, and simplify. Example: Find each product. 1. 2b - 6 b + 1 2. 1 3. d^2 + 3d + 9 3

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Rational Expressions involving Addition and/or Subtraction. First, factor all of the numerators and denominators and determine the Least Common Denominator (LCD). Use the LCD to make both fractions have the same denominator, then add and/or subtract the fractions and simplify. Example: Find each sum or difference. 1. 2.

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Rational Expressions involving Addition and/or Subtraction. First, factor all of the numerators and denominators and determine the Least Common Denominator (LCD). Use the LCD to make both fractions have the same denominator, then add and/or subtract the fractions and simplify. Example: Find each sum or difference. 1. x^2 – 2x x^2 - 16 2. 3y^2 – 2y - 2 6y^2

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Rational Expressions involving Addition and/or Subtraction. Example: Find each sum or difference. 3. 4.

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Rational Expressions involving Addition and/or Subtraction. Example: Find each sum or difference. 3. 7m + 17 m^3 – m^2 – 25 + 1 4. -3a^2 + 3a + 5 a^3 - a

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Complex Fractions. The quotient of two rational expressions is referred to as a Complex Fraction. To simplify, multiply both the numerator and denominator by the LCD of all of the fractions. Example: Simplify the expression.

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Complex Fractions. The quotient of two rational expressions is referred to as a Complex Fraction. To simplify, multiply both the numerator and denominator by the LCD of all of the fractions. Example: Simplify the expression. 5c + 8 c - 4

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Complex Fractions. Example: Simplify the expression.

Section R5: Rational Expressions 223 Reference Chapter Section R5: Rational Expressions Simplifying Complex Fractions. Example: Simplify the expression. 6k - 5 k + 2