Section 6 1 Rational Expressions OBJECTIV ES A

Section 6. 1 Rational Expressions

OBJECTIV ES A Determine the values that make a rational expression undefined.

OBJECTIV ES B Build fractions. C Reduce (simplify) a rational expression to lowest terms.

RULES Avoiding Zero Denominators The variables in a rational expression must not be replaced by numbers that make the denominator zero.

RULES Fundamental Rule of Rational Expressions

PROCEDURE Reducing Rational Expressions to Lowest Terms 1. Write the numerator and denominator of the expression in factored form.

PROCEDURE Reducing Rational Expressions to Lowest Terms 2. Find the factors that are common to the numerator and denominator.

PROCEDURE Reducing Rational Expressions to Lowest Terms 3. Replace the quotient of the common factors by the number 1 since

PROCEDURE Reducing Rational Expressions to Lowest Terms 4. Rewrite the expression in simplified form.

RULE Quotient of Additive Inverses

Chapter 6 Rational Expressions Section 6. 1 Exercise #1

Chapter 6 Rational Expressions Section 6. 1 Exercise #2

Chapter 6 Rational Expressions Section 6. 1 Exercise #3

Section 6. 2 Rational Expressions

OBJECTIV ES A Multiply two rational expressions. B Divide one rational expression by another.

RULE Multiplying Rational Expressions

PROCEDURE Multiplying Rational Expressions 1. Reduce each expression if possible. 2. Multiply the numerators to obtain

PROCEDURE Multiplying Rational Expressions 3. Multiply denominators to obtain new denominator. 4. Reduce if possible.

RULE Dividing Rational Expressions

Chapter 6 Rational Expressions Section 6. 2 Exercise #6

Chapter 6 Rational Expressions Section 6. 2 Exercise #8

Section 6. 3 Rational Expressions

OBJECTIV ES A Add and subtract rational expressions with the same denominator.

OBJECTIV ES B Add and subtract C rational expressions with different denominators. Solve an application.

PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. 1. Find the LCD.

PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. 2. Write all fractions as equivalent ones with LCD as the denominator.

PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. 3. Add or subtract numerators, keep denominators.

PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. 4. Reduce if possible.

Chapter 6 Rational Expressions Section 6. 3 Exercise #11

Chapter 6 Rational Expressions Section 6. 3 Exercise #12

Section 6. 4 Rational Expressions

OBJECTIV EA Simplify a complex fraction using one of two methods.

DEFINITION Complex Fraction A fraction with one or more fractions in its numerator, denominator or both.

PROCEDURE Simplifying Complex Fractions 1. Multiply numerator and denominator by the LCD of the fractions involved, or

PROCEDURE Simplifying Complex Fractions 2. Perform operations indicated in numerator and denominator, then divide simplified numerator by

Chapter 6 Rational Expressions Section 6. 4 Exercise #13

Section 6. 5 Rational Expressions

OBJECTIV ES A Solve equations that contain rational expressions.

OBJECTIV ES B Solve a rational equation for a specified variable.

LEAST COMMON MULTIPLE Multiplying each side of the equation by L is equivalent to multiplying each term by L.

Chapter 6 Rational Expressions Section 6. 5 Exercise #17

Chapter 6 Rational Expressions Section 6. 5 Exercise #18

Section 6. 6 Rational Expressions

OBJECTIV ES A Solve proportions. B Solve applications.

RULE Cross Products

Chapter 6 Rational Expressions Section 6. 6 Exercise #19

Chapter 6 Rational Expressions Section 6. 6 Exercise #21

Chapter 6 Rational Expressions Section 6. 6 Exercise #22

Chapter 6 Rational Expressions Section 6. 6 Exercise #25