Question

Consideram expresia E(x)= ($\frac{1}{ x^{2} -x} - \frac{ 1 }{ x^{2} +x}$ ) : x+2/ x la a 3 a - x
Aratati ca expresia E(x)= 2/x+2

Answer 1

E(x)=[1/(x²-x) - 1/(x²+x)] : (x+2)/(x³-x)=

x³-x=x(x²-1)=x(x-1)(x+1)

=[1/x(x-1) - 1/x(x+1)] : (x+2)/x(x-1)(x+1)=
=(x+1-x+1)/x(x-1)(x+1) × x(x-1)(x+1)/(x+2)=
=(+1+1)/ × /(x+2)=
=2/(x+2)