1. Simplify, Multiply and Divide Rational Expressions
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2. Undefined Values
Any number substituted into a variable which makes the expression in the denominator equal to zero, it will cause the equation to be undefined.
Quick Steps:
FACTOR the expression
Solve the factors in the denominator for the variable
THESE are the restrictions
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3. Example 1
Simplify

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

5. Example 3
Simplify

6. Example 4 (3x + 4) (3x + 4)(x – 1) Simplify
Identify any x-values for which the expression is undefined.
(3x + 4)
(3x + 4)(x – 1)
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7. Example 5
Simplify
Identify any x-values for which the expression is undefined.
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8. 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!!
–1(x2 – 4x)
x2 – 2x – 8
Factor out –1 in the numerator so that x2 is positive, and reorder the terms.
Factor the numerator and denominator. Divide out common factors.
Simplify.
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9. Difference of two Squares!!!
Example 7
Simplify
Factor…Remember
Difference of two Squares!!!
Do NOT
Cancel the “x” or the “3”!!!!!
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10. Example 8
Simplify
If it is not in the order you usually see…switch it!!
REMEMBER…we ALWAYS factor the negative out FIRST when the leading coefficient is NEGATIVE!!!
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11. Rules of Multiplying Expressions
Factor out the GCF of numerator(s) and denominator(s) if possible.
Factor the numerator(s) and denominator (s)
Cancel [up and down OR diagonally] out the factors if needed, multiply and simplify.
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12. Rules of Divide Expressions
Factor the GCF of numerator(s) and denominator(s) if possible.
Take the reciprocal (flip) of the second fraction.
Factor the numerator(s) and denominators into simplest form
Cancel out the factors if needed,
Multiply and simplify
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13. Example 9
Simplify
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14. Example 10 2 2
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15. Example 11
Simplify
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16. Example 12
Simplify
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17. Example 13
Simplify
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18. Example 14
Simplify
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