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

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

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

Basic Expressions & Their Domains Domain (Set Notation) Domain (Interval Notation) 1.4 - Rational Expressions

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

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

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

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

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

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

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

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

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

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

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

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

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

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