Question

Se considera expresia E(x)=(x-1 - x²supra x+2): x-2 supra x+2, unde x este nr real, x≠ -2 si x≠2. Aratati ca E(x)=1, pt orice nr real x, x≠ -2 si x≠2.
Va rooog repede:

Answer 1

 [tex]E(x)=(x-1-\frac{x^2}{x+2}):\frac{x-2}{x+2}= ...\;;\\ (...)=\frac{x^2-x+2x-2\;-\;x^2}{x+2}=\frac{x-2}{x+2}\;\\ \Rightarrow\;E(x}=\frac{x-2}{x+2}:\frac{x-2}{x+2}=1\;\surd\surd[/tex]