Section 6 1 Rational Expressions OBJECTIV ES A
Section 6. 1 Rational Expressions
OBJECTIV ES A Find the numbers that make a rational expression undefined.
OBJECTIV ES B Write an equivalent fraction with the indicated denominator.
OBJECTIV ES C Write a fraction in the standard forms.
OBJECTIV ES D Reduce a fraction to lowest terms.
DEFINITION Rational Expressions If P and Q are polynomials:
DEFINITION Undefined Rational Expressions The variables in a rational expression may not be replaced by values that will make the denominator zero.
DEFINITION Fundamental Property of Fractions If P, Q, and K are polynomials
PROCEDURE Reducing Fractions 1. Write numerator and denominator in factored form. 2. Find the GCF.
PROCEDURE Reducing Fractions 3. Replace the quotient of the common factors by 1. 4. Rewrite in lowest terms.
DEFINITION Quotient of Additive Inverses
Chapter 6 Section 6. 1 A, B Practice Test Exercise #1
Find the undefined value(s) for
Write the fraction with the indicated denominator.
Chapter 6 Section 6. 1 C Practice Test Exercise #2
Write in standard form
Write in standard form
Chapter 6 Section 6. 1 D Practice Test Exercise #4
Reduce to lowest terms. Factor out – 1 Difference of Squares Difference of Cubes
Reduce to lowest terms.
Section 6. 2 Multiplication and Division of Rational Expressions
OBJECTIV ES A Multiply rational expressions.
OBJECTIV ES B Divide rational expressions.
OBJECTIV ES C Use multiplication and division together.
DEFINITION Multiplication of Rational Expressions
PROCEDURE To Multiply Rational Expressions 1. Factor the numerators and denominators completely. 2. Simplify each expression
PROCEDURE To Multiply Rational Expressions 3. Multiply remaining factors. 4. The final product should 5. be in lowest terms.
DEFINITION Division of Real Numbers
Chapter 6 Section 6. 2 B Practice Test Exercise #6
Perform the indicated operations.
Perform the indicated operations.
Chapter 6 Section 6. 2 C Practice Test Exercise #7
Perform the indicated operations.
Perform the indicated operations.
Section 6. 3 Addition and Subtraction of Rational Expressions
OBJECTIV ES A Add or subtract rational expressions with the same denominator.
OBJECTIV ES B Add or subtract rational expressions with different denominators.
PROCEDURE Finding the LCD of Two or More Rational Expressions 1. Factor denominators. Place factors in columns. (Not necessary to factor monomials).
PROCEDURE Finding the LCD of Two or More Rational Expressions 2. Select the factor with the greatest exponent from each column.
PROCEDURE Finding the LCD of Two or More Rational Expressions 3. The product of all the factors obtained is the LCD.
PROCEDURE To Add or Subtract Fractions with Different Denominators. 1. Find the LCD. 2. Write all fractions as 3. equivalent ones with LCD as denominator.
PROCEDURE To Add or Subtract Fractions with Different Denominators. 3. Add numerators. 4. Simplify.
Chapter 6 Section 6. 3 B Practice Test Exercise #9 a
Perform the indicated operations.
Perform the indicated operations.
Perform the indicated operations.
Perform the indicated operations.
Section 6. 4 Complex Fractions
OBJECTIV ES A Write a complex fraction as a simple fraction in reduced form.
PROCEDURE Simplifying Complex Fractions METHOD 1 Multiply the numerator and denominator of the complex fraction by the LCD of all simple
PROCEDURE Simplifying Complex Fractions METHOD 2 Perform operations indicated in numerator and denominator. Then divide numerator by
Chapter 6 Section 6. 4 A Practice Test Exercise #10
Simplify. Multiply by LCD
Simplify.
Simplify.
Section 6. 5 Division of Polynomials and Synthetic Division
OBJECTIV ES A Divide a polynomial by a monomial.
OBJECTIV ES B Use long division to divide one polynomial by another.
OBJECTIV ES C Completely factor a polynomial when one of the factors is known.
OBJECTIV ES D Use synthetic division to divide one polynomial by a binomial.
OBJECTIV ES E Use the remainder theorem to verify that a number is a solution of a given equation.
RULE Dividing a Polynomial by a Monomial Divide each term in the polynomial by the monomial.
DEFINITION The Remainder Theorem
DEFINITION The Factor Theorem
Chapter 6 Section 6. 5 B Practice Test Exercise #13
Divide. Write in descending order.
Divide. Remaind er
Chapter 6 Section 6. 5 C Practice Test Exercise #14
0
Chapter 6 Section 6. 5 E Practice Test Exercise #16
Section 6. 6 Equations Involving Rational Expressions
OBJECTIV ES A Solve equations involving rational expressions.
OBJECTIV ES B Solve applications using proportions.
PROCEDURE Solving Equations Containing Rational Expressions 1. Factor denominators and multiply both sides of the equation by the LCD.
PROCEDURE Solving Equations Containing Rational Expressions 2. Write the result in reduced form. Use the distributive property to remove
PROCEDURE Solving Equations Containing Rational Expressions 3. Determine whether the equation is linear or quadratic and solve accordingly.
PROCEDURE Solving Equations Containing Rational Expressions 4. Check that the proposed solution satisfies the equation. If not, discard it as an
DEFINITION Property of Proportions A proportion is true if the cross products are
Chapter 6 Section 6. 6 A Practice Test Exercise #18
Solve :
Solve : O F F
Chapter 6 Section 6. 6 B Practice Test Exercise #19
a.
Section 6. 7 Applications: Problem Solving
OBJECTIV ES A Solve integer problems.
OBJECTIV ES B Solve work problems.
OBJECTIV ES C Solve distance problems.
OBJECTIV ES D Solve for a specified variable.
PROCEDURE: RSTUV Method for Solving Word Problems Read Select Think Use Verify
Chapter 6 Section 6. 7 B Practice Test Exercise #21
Section 6. 8 Variation
OBJECTIV ES A Direct variation.
OBJECTIV ES B Inverse variation.
OBJECTIV ES C Joint variation.
OBJECTIV ES D Solve applications involving direct, inverse, and joint variation.
DEFINITION Direct Variation y varies directly as x if there is a constant k:
DEFINITION Inverse Variation y varies inversely as x if there is a constant k:
DEFINITION Joint Variation z varies jointly with x and y if there is a constant k:
Chapter 6 Section 6. 8 A Practice Test Exercise #24
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