Question

Buna! Am și eu nevoie de ajutor la expresia aceasta

Answer 1

Salut,

Uite ce simplu este:

$E(x)=\dfrac{2x+1}{x-1}:\left(1-\dfrac{3x^2}{1-x^2}\right)=\dfrac{2x+1}{x-1}:\dfrac{1-x^2-3x^2}{1-x^2}=\\\\=\dfrac{2x+1}{x-1}:\dfrac{1-4x^2}{1-x^2}=\dfrac{2x+1}{x-1}\cdot\dfrac{1-x^2}{1-4x^2}=\dfrac{2x+1}{x-1}\cdot\dfrac{(1-x)(1+x)}{(1-2x)(1+2x)}=\\\\=\dfrac{1}{x-1}\cdot\dfrac{-(x-1)(1+x)}{1-2x}=-\dfrac{1+x}{1-2x}=\dfrac{x+1}{2x-1},\ ceea\ ce\ trebuia\ demonstrat.$

A fost greu ?

Green eyes.