Question

Va rog rapid.
Dau 30 de puncte.

Answer 1

a)

$\it E(x) =\dfrac{(x-2-1)(x-2+1)}{(x-2)(x-3)}+\dfrac{x+2}{(x-2)(x+2)}=\dfrac{(x-3)(x-1)}{(x-2)(x-3)} +\dfrac{1}{x-2}=\\ \\ \\ = \dfrac{x-1+1}{x-2}=\dfrac{x}{x-2}$

b)

$\it E(x)=5 \Rightarrow \dfrac{x}{x-2}=5 \Rightarrow x = 5x-10 \Rightarrow x+10=5x \Rightarrow 5x = x+10 \Rightarrow\\ \\ \Rightarrow 5x-x=10 \Rightarrow 4x=10 \Rightarrow x=\dfrac{10}{4} \Rightarrow x = 2,5$