Simplifying Rational Expressions Lesson 1 Rational Expressions Students

Simplifying Rational Expressions

Lesson 1 Rational Expressions Students will be able to simplify rational expressions Students will be able to multiply and divide rational expressions

Warm Up Factor. 1. 2 x 2 - 3 x + 1 (2 x – 1)(x – 1) 2. 4 x 2 – 9 (2 x – 3)(2 x + 3) 3. 5 x 2 + 6 x + 1 (5 x + 1)(x + 1)

Key Concepts Rational Expression – the quotient of two polynomials. Simplest Form – the numerator and denominator of a rational expression have no common factor

Example 1 What is in simplest form? State restrictions on the variable. Factor Divide out common factors Simplify

Example 2 What is the product in simplest form? State any restrictions on the variable. Factor Divide out common factors Simplify

Example 3 What is the quotient in simplest form? State any restrictions on the variable. Factor Divide out common factors Simplify Multiply by the reciprocal

Lesson 2 Rational Expressions Students will be able to add and subtract rational expressions

Warm Up Add or Subtract. 1. 2.

Key Concepts Steps to Add or Subtract Rational Expressions: 1. Find the LCD of the rational expressions. 2. Write each rational expression as an equivalent rational expression whose denominator is the LCD found in Step 1. 3. Add or subtract numerators, and write the result over the denominator. 4. Simplify resulting rational expression, if possible.

Example 1 What is the least common multiple (LCM) of 2 x 2 - 8 x + 8 and 15 x 2 - 60. Find the prime factors of each expression Identify the greatest power of each factor in each expression Least Common Multiple

Example 2 What is the sum of the two rational expressions in simplest form? Factor Rewrite with a common denominator Simplify Add numerators

Example 3 What is the difference of the two rational expressions in simplest form? Factor Rewrite with a common denominator Simplify Add numerators

Lesson 3 Rational Expressions Students will be able to simplify complex rational expressions

Warm Up Find the least common multiple of the two numbers. 1. 7, 21 21 2. 6, 10 30 3. 11, 17 187

Key Concepts Complex Fraction - a fraction that has a fraction in its numerator or denominator or in both its numerator and denominator.

Example 1 What is the simplest form of the complex fraction? Rewrite with a common denominator Simplify Add Multiply by numerators the reciprocal Simplify

Example 2 What is the simplest form of the complex fraction? Rewrite with a common denominator Simplify Add Multiply by numerators the reciprocal Simplify