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10.1 Simplifying Rational Expressions

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- Goal: to simplify a rational expression

- A “rational expression” is the quotient of two polynomials. (division)

- 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)

- 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)

- 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)

- A factor is in between a multiplication sign
- An addend is in between an addition or subtraction sign
Example:

x + 33x + 9

x – 9 6x + 3

Factor

a-b = -1

b-a