Division of Rational Functions
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4-3-2017
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Just like rational number division (division of regular fractions), multiply the inverse or the reciprocal. This process is also called "INVERT AND MULTIPLY." For example, suppose you had to divide 1/2 by 3/7. The typical procedure reminds us to "never mind the reason why, just invert and multiply." So following that rule you multiply 1/2 times 7/3 to arrive at the answer of 7/6. This same procedure can be used to divide rational functions.
Sample:
(x + 1)/(x + 3) DIVIDED by (3x + 3)/(x - 2)
1) Invert right side fraction.
The right side fraction should then look like this: (x - 2)/(3x + 3).
2) Replace division symbol with multiplication symbol (because never mind the reason why, just invert and multiply).
3) Multiply numerator by numerator and denominator by denominator using the FOIL Method.
Numerator: (x + 1) ( x - 2) becomes x 2 - x - 2
Denominator (x + 3) (3x + 3) becomes 3x 2 + 12x + 9
4) Reduce fraction (if needed)
Final answer: (x 2 - x - 2)/(3x 2 + 12x + 9)
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