1. 11.1 Simplifying Rational Expressions
Goal: to simplify a rational expression
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2. Simplifying Rational Expressions
A “rational expression” is the quotient of two polynomials. (division)
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3. Simplifying Rational Expressions
A “rational expression” is the quotient of two polynomials. (division)
A rational expression is in simplest form when the numerator and denominator have no common factors (other than 1)
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4. Simplifying Rational Expressions
A “rational expression” is the quotient of two polynomials. (division)
A rational expression is in simplest Form when the numerator and denominator have no common factors (other than 1)
We can not cancel the 3 because there is addition/subtraction included. We can only cancel if we have multiplication.
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5. Simplifying Rational Expressions
Again, we can not cancel a 3 because there is addition/subtraction included. We can only cancel if we have multiplication.
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6. How to get a rational expression in simplest form…
Factor the numerator completely (factor out a common factor, difference of 2 squares, bottoms up)
Factor the denominator completely (factor out a common factor, difference of 2 squares, bottoms up)
Cancel out any common factors (not addends)
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7. How to write the domain with constrains…
The constrain(s) of a rational expression is a number(s) that cannot be included in the domain because it will make the denominator equal to zero.
In x x – 9 ≠ 0 Thus x ≠ 9.
x – our domain is D:{ x | (-∞, 9) U (9, ∞)
In 3x x + 3 ≠ 0 Thus x ≠ -1/2.
6x our domain is D:{ x | (-∞, -1/2) U (-1/2, ∞)}
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8. Difference between a factor and an addend
A factor is in between a multiplication sign
An addend is in between an addition or subtraction sign
Example:
x x + 9
x – x + 3
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9. Factor *Remember The denominator can never = 0. Our constraint is:
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10. The denominator can never = 0.
*Remember
The denominator can never = 0.
Our constraints are:
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11. The denominator can never = 0.
*Remember
The denominator can never = 0.
Our constraint is:
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12. *Do not forget to include your constrains:
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13. *Do not forget to include your constrains:
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14. *Do not forget to include your constrains:
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15. *Do not forget to include your constrains:
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16. Taken and modified from http://podcasts. shelbyed. k12. al

17. Taken and modified from http://podcasts. shelbyed. k12. al