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x^4-4=(x²-2)(x²+2)=(x-√2)(x+√2)(x²+2) x²-(√2-1)x-√2=(x-1)(x+√2) x1+x2=-1+√2 U x1*x2=-√2 x1=-1 U x2=+√2 ---------------------------------- (x-√2)(x+√2)(x²+2)/(x²+2)(x+1)(x-√2)=(x+√2)/(x+1)

[latex] \frac{x^4-4}{(x^2+2)(x^2- (\sqrt{2}-1)x- \sqrt{2}) } = \frac{(x^2-2)(x^2+2)}{(x^2+2)(x^2- x\sqrt{2}+x- \sqrt{2}) }=\frac{x^2-2}{x(x+1)- \sqrt{2}(x+1) }= \\ = \frac{(x-\sqrt{2})(x+\sqrt{2})}{(x- \sqrt{2})(x+1) }=\frac{x+\sqrt{2}}{x+1 }[/latex]