Question

Fie raportul F(x)= x^3 + x^2-4x-4 supra x^3- 4x.
a) arătat-o ca f(x)=x+1 supra x.
(semnul ^ înseamnă ridicarea la putere)

Answer 1

(x³+x²-4x-4)(x³-4x)=(x³-4x)/(x³-4)+(x²-4)/x(x²-4)=1+1/x=(x+1)/x
E(x)=(x+1)/x

Answer 2

Stabilim dom.de definitie:
x³-4x
x(x²-4)≠0=>x≠0;x≠ +2 x≠ -2
F(x)=$\frac{x^{3}+x^{2}-4x-4}{x^{3}-4x} = \frac{x^{2}(x+1)-4(x+1)}{x(x^{2}-4)} =\ \textgreater \ F(x)= \frac{(x+1)(x^{2}-4)}{x(x^{2}-4)} =\ \textgreater \ F(x)= \frac{x+1}{x}$
Am descopus la numarator:
x³+x²-4x-4
x²(x+1)-4(x+1)= (x+1)(x²-4)
Iar la numitor am descompus:
x³-4x
x(x²-4)