Упростить выражение:[tex] \frac{ x^{3}- x^{2} -x+1 }{ x^{4}- x^{3}-3 x^{2} +5x-2 } [/tex]Ответ: [tex] \frac{x+1}{ x^{2} +x-2} [/tex]. Created by nikolson93. algebra-ru

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Упростить выражение:
[tex] \frac{ x^{3}- x^{2} -x+1 }{ x^{4}- x^{3}-3 x^{2} +5x-2 } [/tex]
Ответ: [tex] \frac{x+1}{ x^{2} +x-2} [/tex]

Yura13 $= \frac{ x^{2} (x-1)-(x-1) }{ x^{4} - x^{3} -3 x^{2} +3x+2x-2} = \\ = \frac{(x-1)( x^{2} -1)}{ x^{3}(x-1)-3x(x-1)+2(x-1) } =\\ = \frac{(x-1)( x^{2} -1)}{(x-1)( x^{3}-3x+2 )}= \\ = \frac{ x^{2} -1}{ x^{3}-3x+2} = \\ = \frac{(x-1)(x+1)}{ x^{3}-x-2x+2 }= \\ = \frac{(x-1)(x+1)}{(x-1)( x^{2} +x-2)} =\\= \frac{x+1}{ x^{2} +x-2}$

1 votes Thanks 2

неизвестна (x-1)(x2-1)/(x-1)(x3-3x+2)=x2-1/x3-3x+2=(x+1)(x-1)/x3-x-2x+2=(x-1)(x+1)/(x-1)(x2-x-2)=x+1/x2+x-2
Ответ:x+1/x2+x-2

0 votes Thanks 1

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semya uilyams sostoit iz papy mamy i neskolkih detej srednij vozrast vseh chle

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