E(x) = [tex](\frac{x^{2}+4}{2x}-2):(\frac{2x^{2}+4x}{x^{2}+4x+4}-1)*(\frac{1}{x+2}+\frac{1}{x-2})[/tex]
= (x² + 4 - 4x)/2x · (x² + 4x + 4)/(2x² + 4x - x² - 4x - 4) · (x - 2 + x + 2)/(x² - 4)
= (x - 2)²/2x · (x + 2)²/(x² - 4) · 2x/(x² - 4)
= (x - 2)(x - 2)(x + 2)(x + 2)/(x - 2)(x + 2)(x - 2)(x + 2)
= 1
(E(x) - 2)¹⁰⁰ = (1 - 2)¹⁰⁰ = (- 1)¹⁰⁰ = 1
