Question

Pentru xe R-{+-4} ,aduceti expresia la forma cea mai simpla,unde :
E(x)=x patrat -4 / x patrat + 5x +6 * x patrat +6x +9 / x patrat +2x-8 - x+1 / x-4 - 8 / x patrat -16

Answer 1

Obs:  x²-4=(x+2)(x-2)
Obs: x²+5x+6=(x+2)(x+3)
Obs:  x²+6x+9=(x+3)²
Obs: x²+2x-8=(x-2)(x+4)
Obs: x²-16=(x-4)(x+4)
E(x)=[(x+2)(x-2)/(x+2)(x+3)]·[(x+3)²/(x-2)(x+4)]-(x+1)/(x-4)-8/(x²-16)   simplificam cu x+2
E(x)=[(x-2)/(x+3)]·[(x+3)²/(x-2)(x+4)-(x+1)/(x-4)]-8/(x²-16)   simplificam cu x-2
E(x)=[1/(x+3)]·[(x+3)²/(x+4)]-(x+1)/(x-4)-8/(x²-16)   simplificam cu x+3
E(x)=(x+3)/(x+4)-(x+1)(x-4)-8/(x-4)(x+4)  aducem la acelasi numitor
E(x)=[(x+3)(x-4)-(x+1)(x+4)-8]/(x-4)(x+4)
E(x)=[x²-4x+3x-12-(x²+4x+x+4)-8]/(x-4)(x+4)
E(x)=[x²-x-12-x²-5x-4-8]/(x-4)9x+4)
E(x)=(-6x-24)/(x-4)(x+4)
E(x)=-6(x+4)/(x-4)(x+4)   simplificam cu x+4
E(x)=-6/(x-4)