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Exercutiul 6, va rogg

Exercutiul 6 Va Rogg class=

Răspuns :

(x²-2x)/[(x-3)²-1]= x(x-2)/[(x-3-1)(x-3+1)]=x(x-2)/[(x-4)(x-2)]=x/(x-4)

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[tex]\displaystyle \\ E(x)= \frac{x^2-2x}{(x-3)^2-1} = \\ \\ \\ = \frac{x(x-2)}{x^2-6x +9 -1} = \\ \\ \\ = \frac{x(x-2)}{x^2-6x +8} = \\ \\ \\ = \frac{x(x-2)}{\underbrace{x^2-2x} - \underbrace{4x +8}} = \\ \\ \\ = \frac{x(x-2)}{x(x-2) - 4(x -2)} = \\ \\ \\ = \frac{x(x-2)}{(x-2)( x- 4)} = \boxed{\frac{x}{ x- 4} }[/tex]



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