Question

Se considera expresia E(x)=( 1 + 2-x supra x+1 ) : x-1 supra (2x+1)²- (x+2)²,unde x este numar real ,x≠1 si x≠-1.Aratati ca E(x)=9

Answer 1

1+(2-x)/(x+1)= (x+1+2-x)/(x+1)=3/(x+1)
(2x+1)²-(x+2)²=[(2x+1)+(x+2)]·[(2x+1)-(x+2)]= 3(x+1)(x-1)

$(1+ \frac{2-x}{x+1} ): \frac{ x-1 }{ (2x+1)^{2} - (x+2)^{2} } =$
$\frac{3}{x+1}: \frac{x-1}{3(x+1)(x-1)} =$
$\frac{3}{x+1}: \frac{1}{3(x+1)} =$
$\frac{3}{x+1}* 3(x+1)$=9