1 Topic 8.2.2 Dividing Rational Expressions Dividing Rational Expressions.
CHAPTER 6 Rational Expressions and Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson...
19
-
Upload
diana-cameron -
Category
Documents
-
view
216 -
download
3
Transcript of CHAPTER 6 Rational Expressions and Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson...
CHAPTER
6Rational Expressions and Equations
Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
6.1 Multiplying and Simplifying Rational Expressions
6.2 Division and Reciprocals
6.3 Least Common Multiples and Denominators
6.4 Adding Rational Expressions
6.5 Subtracting Rational Expressions
6.6 Complex Rational Expressions
6.7 Solving Rational Equations
6.8 Applications Using Rational
6.9 Variation and Applications
OBJECTIVES
6.5 Subtracting Rational Expressions
aMultiply
monomials.
Slide 3Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
a Subtract rational expressions.b Simplify combined additions and subtractions of
rational expressions.
6.3Least Common Multiples and Denominators
a
6.5 Subtracting Rational Expressions
aSubtract rational
expressions.
Finding LCMs
Subtracting Rational Expressions with Like Denominators
Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 4Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
To subtract when the denominators are the same, subtract the numerators and keep the same denominator. Then simplify if possible.
EXAMPLE
6.5 Subtracting Rational Expressions
a Subtract rational expressions.
2 Subtract:
Slide 5Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
6.5 Subtracting Rational Expressions
aSubtract rational
expressions.
Subtracting Rational Expressions with Different Denominators
Slide 6Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
To subtract rational expressions with different denominators:1. Find the LCM of the denominators. This is the least
common denominator (LCD).2. For each rational expression, find an equivalent expression
with the LCD. To do so, multiply by 1 using a symbol for 1 made up of factors of the LCD that are missing from the original denominator.
3. Subtract the numerators. Write the difference over the LCD.
4. Simplify if possible.
EXAMPLE
6.5 Subtracting Rational Expressions
a Subtract rational expressions.
3 Subtract:
Slide 7Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
6.5 Subtracting Rational Expressions
a Subtract rational expressions.
3 Subtract:
Slide 8Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
6.5 Subtracting Rational Expressions
a Subtract rational expressions.
6 Subtract:
Slide 9Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE Solution
6.5 Subtracting Rational Expressions
a Subtract rational expressions.
6
Slide 10Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE Solution
6.5 Subtracting Rational Expressions
a Subtract rational expressions.
6
Slide 11Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
6.5 Subtracting Rational Expressions
a Subtract rational expressions.
7 Subtract:
Slide 12Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
Factoring 64 – p2, we get (8 – p)(8 + p).Note that the factors 8 – p in the first denominator and p – 8 in the second denominator are opposites.
EXAMPLE Solution
6.5 Subtracting Rational Expressions
a Subtract rational expressions.
7
Slide 13Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE Solution
6.5 Subtracting Rational Expressions
a Subtract rational expressions.
7
Slide 14Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
6.5 Subtracting Rational Expressions
bSimplify combined additions and subtractions of rational expressions.
8 Perform the indicated operations and simplify:
Slide 15Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE Solution
6.5 Subtracting Rational Expressions
bSimplify combined additions and subtractions of rational expressions.
8
Slide 16Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE
6.5 Subtracting Rational Expressions
bSimplify combined additions and subtractions of rational expressions.
9 Perform the indicated operations and simplify:
Slide 17Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE Solution
6.5 Subtracting Rational Expressions
bSimplify combined additions and subtractions of rational expressions.
9
Slide 18Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
EXAMPLE Solution
6.5 Subtracting Rational Expressions
bSimplify combined additions and subtractions of rational expressions.
9
Slide 19Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc.
