Question

Ex 2 partea a lll a dau coroana

Answer 1

a)

$E(x) = \frac{x^3}{x-1}*(\frac{1}{x^2}-\frac{1}{x^4})-\frac{x+3}{x}\\ E(x) = \frac{x^3}{x-1}*\frac{1}{x^2}-\frac{x^3}{x-1}*\frac{1}{x^4}-\frac{x+3}{x}\\ E(x) = \frac{x}{x-1}-\frac{1}{x(x-1)} -}\frac{x+3}{x}$

Amplifici prima fractie cu x si pe a treia cu x-1

$E(x) = \frac{x^2-1-(x+3)(x-1)}{x(x-1)} =\frac{x^2-1-x^2+x-3x+3}{x(x-1)}=\frac{-2x+2}{x(x-1)}=\frac{-2(x-1)}{x(x-1)}= \frac{-2}{x}$

b) E(n) = -2/n apartine Z

Solutiile potrivite pentru n sunt {-2, -1, 0, 1, 2}