(4/x^2-4+1/2-x)*x^2+4x+4/3

Question

(4/x^2-4+1/2-x)*x^2+4x+4/3

Answer 1

(4/(x²-4) +1/(2-x)) *(x²+4x+4)/3

1) в скобках
x² -4 =(x -2)(x +2)
2 -x = -(x -2)

(4 -(x+2)) /(x-2)(x+2) =(4 -x -2) /(x -2)(x +2) = -(x -2) /(x -2)(x +2) = -1/(x +2)

2) (x² +4x +4)/3 =(x +2)²/3

3) -1/(x+2) * (x+2)²/3 = -(x+2)² /(x+2)*3 = -(x+2)/3

ответ: -(x+2)/3