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Section 6.1 Rational Expressions
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OBJECTIVES Determine the values that make a rational expression undefined. A
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OBJECTIVES Build fractions.
Reduce (simplify) a rational expression to lowest terms. C
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RULES Avoiding Zero Denominators
The variables in a rational expression must not be replaced by numbers that make the denominator zero.
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RULES Fundamental Rule of Rational Expressions
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PROCEDURE Reducing Rational Expressions to Lowest Terms
Write the numerator and denominator of the expression in factored form.
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PROCEDURE Reducing Rational Expressions to Lowest Terms
Find the factors that are common to the numerator and denominator.
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PROCEDURE Reducing Rational Expressions to Lowest Terms
Replace the quotient of the common factors by the number 1 since
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PROCEDURE Reducing Rational Expressions to Lowest Terms
Rewrite the expression in simplified form.
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RULE Quotient of Additive Inverses
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Section 6.1 Exercise #1 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Let’s work Exercise #19 from Section 5.1
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Section 6.1 Exercise #2 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Let’s work Exercise #19 from Section 5.1
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Section 6.1 Exercise #3 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Let’s work Exercise #19 from Section 5.1
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Section 6.2 Rational Expressions
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OBJECTIVES Multiply two rational expressions.
Divide one rational expression by another. B
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RULE Multiplying Rational Expressions
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PROCEDURE Multiplying Rational Expressions
Reduce each expression if possible. Multiply the numerators to obtain the new numerator.
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PROCEDURE Multiplying Rational Expressions
Multiply denominators to obtain new denominator. Reduce if possible.
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RULE Dividing Rational Expressions
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Section 6.2 Exercise #6 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Section 6.2 Exercise #8 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Section 6.3 Rational Expressions
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OBJECTIVES Add and subtract rational expressions with the same denominator. A
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OBJECTIVES Add and subtract rational expressions with different denominators. B Solve an application. C
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PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Find the LCD.
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PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Write all fractions as equivalent ones with LCD as the denominator.
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PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Add or subtract numerators, keep denominators.
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PROCEDURE Adding (or Subtracting) Fractions with Different Denominators. Reduce if possible.
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Section 6.3 Exercise #11 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Section 6.3 Exercise #12 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Section 6.4 Rational Expressions
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OBJECTIVE Simplify a complex fraction using one of two methods. A
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DEFINITION Complex Fraction
A fraction with one or more fractions in its numerator, denominator or both.
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PROCEDURE Simplifying Complex Fractions
Multiply numerator and denominator by the LCD of the fractions involved, or
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PROCEDURE Simplifying Complex Fractions
Perform operations indicated in numerator and denominator, then divide simplified numerator by simplified denominator.
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Section 6.4 Exercise #13 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Section 6.5 Rational Expressions
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OBJECTIVES Solve equations that contain rational expressions. A
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OBJECTIVES B Solve a rational equation for a specified variable.
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LEAST COMMON MULTIPLE Multiplying each side of the equation
by L is equivalent to multiplying each term by L.
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Section 6.5 Exercise #17 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Section 6.5 Exercise #18 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Section 6.6 Rational Expressions
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OBJECTIVES Solve proportions. A Solve applications. B
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RULE Cross Products
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Section 6.6 Exercise #19 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Section 6.6 Exercise #21 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Section 6.6 Exercise #22 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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Section 6.6 Exercise #25 Chapter 6 Rational Expressions
Let’s work Exercise #19 from Section 5.1
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