8.2.1 Simplify rational expressions.

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8-2 LEARNING GOALS
8.2.1 Simplify rational expressions. 8.2.2
Multiply and divide rational expressions.
A ___________ ____________is a quotient of two
polynomials. Examples
You can simplify rational expressions the same
way as you simplify fractions. How do you write
a fraction in simplest form? Examples
We know that when ____ is in the denominator the
fraction is undefined. When you have a
______________ in the denominator you must
consider what values will make the denominator
____ because it makes the function undefined for
that value.
Example 1 Simplifying Rational Expressions
Simplify. Identify any x-values for which the
expression is undefined.
A.
B.
X ? ___________
X ? ___________
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2
Simplify. Identify any x-values for which the
expression is undefined.
C.
D.
X ? ___________
X ? ___________
Example 2 Simplifying by Factoring by 1
Simplify. Identify any x values for which the
expression is undefined.
A.
B.
X ? ___________
X ? ___________
C.
X ? ___________
Check the calculator table.
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Example 3 Multiplying Rational Expressions
A.
Multiply. Assume that all expressions are defined.
B.
C.
D.
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Example 4 Dividing Rational Expressions
Divide. Assume that all expressions are defined.
A.
B.
C.
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Example 5 Solving Simple Rational Equations
Solve. Check your solution.
A.
X ? ___________
Final Answer ______________
B.
X ? ___________
Final Answer ______________
C.
X ? ___________
Final Answer ______________
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