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

2. 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

3. 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

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

5. 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

6. 1.4 - Rational Expressions
Example 1
Simplify the following expression.
1.4 - Rational Expressions

7. 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

8. 1.4 - Rational Expressions
Example 2
Perform the multiplication and simplify.
1.4 - Rational Expressions

9. 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

10. 1.4 - Rational Expressions
Example 3 – pg. 42 #33
Perform the multiplication and simplify
1.4 - Rational Expressions

11. 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

12. 1.4 - Rational Expressions
Example 4 – pg. 42 #48
Perform the addition or subtraction and simplify.
1.4 - Rational Expressions

13. 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

14. 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

15. 1.4 - Rational Expressions
Example 5 – pg. 42 #60
Perform the addition or subtraction and simplify.
1.4 - Rational Expressions

16. 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

17. 1.4 - Rational Expressions
Example 6 – pg. 43 #81
Rationalize the denominator.
1.4 - Rational Expressions

18. 1.4 - Rational Expressions
Example 7 – pg. 43 #87
Rationalize the numerator.
1.4 - Rational Expressions