Skróć ułamki. Podaj konieczne założenia.
a.) (X-1)^2+ 4x / x^2 -1
b.) 4-(x-2)^2 / 16x-8x^2+x^3
a/ (x-1)²+4x/(x²-1)= (x-1)(x-1)+4x/(x-1)(x+1)=(x-1)+4x/(x+1) = (x-1)(x+1)+4x(x+1)/(x+1)=(x-1)(x+1)+4x=x²-1+4x=x²+4x-1
b/ 4-(x-2)²/16x-8x²+x³= 4-(x²-4x+4)/x(x²-8x+16)=4-(x-2)²/x(x-4)²=-x²+4x/x(x-4)²=
-x(x-4)/x(x-4)²=-1/x-4
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a/ (x-1)²+4x/(x²-1)= (x-1)(x-1)+4x/(x-1)(x+1)=(x-1)+4x/(x+1) = (x-1)(x+1)+4x(x+1)/(x+1)=(x-1)(x+1)+4x=x²-1+4x=x²+4x-1
b/ 4-(x-2)²/16x-8x²+x³= 4-(x²-4x+4)/x(x²-8x+16)=4-(x-2)²/x(x-4)²=-x²+4x/x(x-4)²=
-x(x-4)/x(x-4)²=-1/x-4