Question

Найдите числовое значение выражения
4/x2+4x+4 : (x2+12/x2-4 - x+2/x-2) при x = -1

Answer 1

1) 4/(x²+4x+4)=4/(x+2)².

2) (x²+12)/(x²-4)-(x+2)/(x-2)=(x²+12)/((x-2)(x+2))-(x+2)/(x-2)=

=(x²+12-(x+2)²)/((x+2)(x-2))=(x²+12-x²-4x-4)/((x+2)(x-2))=(-4x-8)/((x+2)(x-2))=

=-4*(x-2)/((x+2)(x-2))=-4/(x+2).

3) (4/(x+2)²):(-4/(x+2))=4*(x+2)/(-4*(x+2)²)=-1/(x+2)=-1/(-1+2)=-1/1=-1.