 # Section 6.1 Rational Expressions.

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Section 6.1 Rational Expressions

OBJECTIVES Determine the values that make a rational expression undefined. A

OBJECTIVES Build fractions.
Reduce (simplify) a rational expression to lowest terms. C

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
Write the numerator and denominator of the expression in factored form.

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

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

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

Section 6.1 Exercise #1 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Let’s work Exercise #19 from Section 5.1

Section 6.1 Exercise #2 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Let’s work Exercise #19 from Section 5.1

Section 6.1 Exercise #3 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Let’s work Exercise #19 from Section 5.1

Section 6.2 Rational Expressions

OBJECTIVES Multiply two rational expressions.
Divide one rational expression by another. B

RULE Multiplying Rational Expressions

PROCEDURE Multiplying Rational Expressions
Reduce each expression if possible. Multiply the numerators to obtain the new numerator.

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

RULE Dividing Rational Expressions

Section 6.2 Exercise #6 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Section 6.2 Exercise #8 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Section 6.3 Rational Expressions

OBJECTIVES Add and subtract rational expressions with the same denominator. A

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

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

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

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

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

Section 6.3 Exercise #11 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Section 6.3 Exercise #12 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Section 6.4 Rational Expressions

OBJECTIVE Simplify a complex fraction using one of two methods. A

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

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

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

Section 6.4 Exercise #13 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Section 6.5 Rational Expressions

OBJECTIVES Solve equations that contain rational expressions. A

OBJECTIVES 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.

Section 6.5 Exercise #17 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Section 6.5 Exercise #18 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Section 6.6 Rational Expressions

OBJECTIVES Solve proportions. A Solve applications. B

RULE Cross Products

Section 6.6 Exercise #19 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Section 6.6 Exercise #21 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Section 6.6 Exercise #22 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1

Section 6.6 Exercise #25 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1