Transcript Multiplying Rational Expressions

Multiplying Rational
Expressions
Topic 8.2.1
1
Lesson
Topic
1.1.1
8.2.1
Multiplying Rational Expressions
California Standard:
What it means for you:
13.0 Students add, subtract, multiply,
and divide rational expressions and
functions. Students solve both
computationally and conceptually
challenging problems by using these
techniques.
You’ll multiply rational
expressions by factoring
and cancelling.
Key words:
• rational
• nonzero
• common factor
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Lesson
Topic
1.1.1
8.2.1
Multiplying Rational Expressions
In Section 8.1 you learned about simplifying
rational expressions.
In this Topic you’ll learn to multiply rational expressions,
but then you’ll use the same simplification methods to
express your solutions in their simplest forms.
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Lesson
Topic
1.1.1
8.2.1
Multiplying Rational Expressions
Multiplying by Rational Expressions
Given any nonzero expressions m, c, b, and v:
That is, the product of two rational expressions is the
product of the numerators divided by the product
of the denominators.
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Lesson
Topic
1.1.1
8.2.1
Multiplying Rational Expressions
Multiplying by Rational Expressions
These expressions can often be quite complicated,
so simplify them as much as you can before multiplying.
• First, factor the numerators and denominators
(if possible).
• Then find any factors that are common to both the top
line (the numerator) and the bottom line (the denominator)
and cancel them before multiplying.
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Topic
Multiplying Rational Expressions
8.2.1
Example
1
Simplify
.
Solution
Step 1: Factor the numerators and denominators.
=
Step 2: Cancel all the common factors and multiply.
1
=
1
1
1
1
1
=
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Solution follows…
Topic
Multiplying Rational Expressions
8.2.1
Example
2
Multiply and simplify
.
Solution
Step 1: Factor the numerators and denominators if possible.
=
=
Step 2: Cancel all the common factors and multiply.
1
=
1
1
1
1
1
1
1
1= –
2
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Solution follows…
Lesson
Topic
1.1.1
8.2.1
Multiplying Rational Expressions
Guided Practice
Multiply and simplify the rational expressions.
1.
2.
3.
4.
5.
6.
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Solution follows…
Lesson
Topic
1.1.1
8.2.1
Multiplying Rational Expressions
You can extend this concept to the multiplication
of any number of rational expressions, with any
number of variables.
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Topic
Multiplying Rational Expressions
8.2.1
Example
3
Simplify
.
Solution
Factor the numerators and denominators,
and cancel all the common factors and multiply.
1
11
=
=
1
1 1
=
1
1
1
1
1
1
or
10
Solution follows…
Topic
Multiplying Rational Expressions
8.2.1
Example
4
Simplify
.
Solution
Factor the numerators and denominators,
then cancel all the common factors and multiply.
1
=
=
1 1
1
1
11
1
or
11
Solution follows…
Lesson
Topic
1.1.1
8.2.1
Multiplying Rational Expressions
Guided Practice
Multiply and simplify the rational expressions.
7.
x–5
8.
2(m + 1) or 2m + 2
9.
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Solution follows…
Topic
8.2.1
Multiplying Rational Expressions
Independent Practice
Multiply and simplify the rational expressions.
1.
2.
3.
1
4.
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Solution follows…
Topic
8.2.1
Multiplying Rational Expressions
Independent Practice
Multiply and simplify the rational expressions.
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Solution follows…
Topic
8.2.1
Multiplying Rational Expressions
Round Up
Usually the most difficult thing when solving
problems like these is factoring the numerators
and denominators.
Look for “difference of two squares”
expressions, perfect squares, and minus signs
that you can factor outside the parentheses.
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