1. Simplify, Multiply and Divide Rational Expressions
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2. Example 1
Simplify

3. Example 2 Simplify 2 1 2 1 Subtract exponents
variable stays where largest exponent is 1

4. Example 3
Simplify 8 5

5. Solve the factors (before cancelling) by setting them equal to zero
Restrictions: Any value that makes the rational expression undefined (results in a zero in the denominator)
Factor the expression
Solve the factors (before cancelling) by setting them equal to zero
The results are the restrictions
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6. Example 4
Simplify
Identify any x-values for which the expression is undefined.
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7. Example 6
Simplify Identify any x-values for which the expression is undefined.
If it is not in the order you usually see…switch it!!
Factor out –1 in the numerator so that x2 is positive, and reorder the terms.
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8. Example 7 Simplify Do NOT Cancel the “x” or the “3”!!!!!
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9. Rules of Multiplying Expressions
Factor numberator(s) and denominator(s)
Extend the fraction bar
Cancel [top/bottom] out the factors if needed and simplify.
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10. Rules of Divide Expressions
KFC!!! Keep it (the first fraction), Flip it (the second fraction), Change it (the sign – division becomes multiplication)
Multiply and simplify!
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11. Example 9
Simplify
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12. Example 10
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13. Example 11
Simplify
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14. Example 12
Simplify
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