## Simplifying Rational Functions: (x^4-3x^3-5x^2-7x+9)/(x^5-x^

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
gem1110000
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### Simplifying Rational Functions: (x^4-3x^3-5x^2-7x+9)/(x^5-x^

X4-3X3-5X2-7X+9
------------------------
X5-X4-X3+3X2+5X+18

Help me this is so confusing to me!

stapel_eliz
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On what basis had you concluded that either of these polynomials was factorable...?

gem1110000
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### Re: Simplifying Rational Functions: (x^4-3x^3-5x^2-7x+9)/(x^5-x^

Ha the back of the book says (1/X+2) so I wana know how they got there.

Martingale
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### Re: Simplifying Rational Functions: (x^4-3x^3-5x^2-7x+9)/(x^5-x^

did you type the question in correctly?

gem1110000
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### Re: Simplifying Rational Functions: (x^4-3x^3-5x^2-7x+9)/(x^5-x^

oh dang its supposed to be +5x^2 in the top equation.

stapel_eliz
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oh dang its supposed to be +5x^2 in the top equation.
Okay, well... now it appears that the numerator has no real factors, rational or otherwise.

gem1110000
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### Re: Simplifying Rational Functions: (x^4-3x^3-5x^2-7x+9)/(x^5-x^

WOW I feel so dumb right now it was just long division................

stapel_eliz
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I feel so dumb right now it was just long division.
Um... how are you supposed to do that...?

Since the denominator (the divisor) has a larger degree than the numerator (the dividend), you can't actually do any polynomial long division, at least not as currently presented.

Was the exercise perhaps to divide $x^5\, -\, x^4\, -\, x^3\, +\, 4x^2\, -\, 5x\, +\, 18$ by $x^4\, -\, 3x^3\, +\, 5x^2\, -\, 7x\, +\, 9$...? Because then the answer would be $x\, +\, 2$.