Simplifying Rational Expressions

Simplifying Rational Expressions

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

Warm Up Factor. 1. 2x2 - 3x 1 2. 4x2 – 9 3. 5x2 6x 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 x 2 - 6 x - 16 the variable. form? State x 2 5 xin simplest 6 restrictions on

Example 2 x 2 - 25 What is the product i x 2 x - 6 x 4 x 3 in simplest x - 5 form? State 2 any restrictions on the variable.

Example 3 What is the quotient x 2 5x 4 2 x x - 12 any restrictions on the variable. x2-1 in simplest form? State 2 2x - 6x

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

Warm Up Add or Subtract. 1. 5 7 19 38 2. 2 15 - 3 25

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 2x2 - 8x 8 and 15x2 - 60.

Example 2 What is the sum of the two rational expressions in simplest form? 1 4x 2 3 x 2 1x 3 0 3 x 15

Example 3 What is the difference of the two rational expressions in simplest form? 2x 3 2 x - 2x - 3 - 4x 4

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 2. 6, 10 3. 11, 17

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? 1 x 2 y 1 y - 1 x

Example 2 What is the simplest form of the complex fraction? -3 5 x y