Răspuns:
Explicație pas cu pas:
[tex]E(x)=(\frac{1+x^{2} }{1-x^{2} } -\frac{1-x^{2} }{1+x^{2} }) :(\frac{1+x}{x-x^{2} } -\frac{1-x}{x+x^{2} } )\\[/tex]
aducem la acelasi numitor in paranteze si vom obtine
[tex]E(x)=(\frac{(1+x^{2} )(1+x^{2} )-(1-x^{2} )(1-x^{2} )}{(1-x^{2} )(1+x^{2} )} ):(\frac{(1+x)(1+x)-(1-x)(1-x)}{x(1-x)(1+x)} )[/tex]
[tex]E(x)=(\frac{1+2x^{2} +x^{4}-1+2x^{2} -x^{4} }{(1-x^{2} )(1+x^{2} )} ):(\frac{1+2x+x^{2} -1+2x-x^{2} }{x(1-x)(1+x)} )[/tex]
[tex]E(x)=(\frac{4x^{2} }{(1-x )(1+x)(1+x^{2} )} )\cdot \frac{x(1-x)(1+x)}{4x}[/tex]
[tex]E(x)=\frac{x^{2} }{1+x^{2} }[/tex]
