Question

Se considera fractia algebrica :
F(x) = x⁴+4x²+3/ x⁴+2x-3

Aratati ca F(x) = x²+1/ x²-1

Answer 1

$x^4+4x^2+3=x^4+3x^2+x^2+3=x^2(x^2+1)+3(x^2+1)=\\=(x^2+1)(x^2+3). \\ x^4+2x^2-3=x^4+3x^2-x^2-3=x^2(x^2-1)+3(x^2-1)= \\ = (x^2-1)(x^2+3)$
Simplificand pe (x²+3) obtinem concluzia.