Question

simplificati raportul (x patrat+2x)(2x-6+x patrat) +8 supra (x patrat + 2x)( 2x-7+x patrat) +12

Answer 1

[tex]E(x)=\dfrac{(x^2+2x)(2x-6+x^2)+8}{(x^2+2x)(2x-7+x^2)+12}\\ Notam: x^2+2x=t\\ E(x)=\dfrac{t(t-6)+8}{t(t-7)+12}\\ E(x)=\dfrac{t^2-6t+8}{t^2-7t+12}\\ ---------\\ *t^2-6t+8=t^2-4t-2t+8=t(t-4)-2(t-4)=(t-4)(t-2)\\ t^2-7t+12=t^2-3t-4t+12=t(t-3)-4(t-3)=(t-3)(t-4)\\ E(x)=\dfrac{(t-4)(t-2)}{(t-3)(t-4)}=\dfrac{t-2}{t-3}\\ \boxed{E(x)=\dfrac{x^2+2x-2}{x^2+2x-3} ,\forall x\in \mathbb{R}\backslash \{3,4\}}[/tex]