Question

4x supra x+3 - x supra x-3=12 supra 9-x la puterea a 2

Answer 1

Formule de calcul prescurtat:

(A+B)^2=A^2+2AB+B^2

(A-B)^2=A^2-2AB+B^2

(A+B)(A-B)=A^2-B^2

4x/(x+3)-x/(x-3)=12/(9-x)^2

4x/(x+3)-x/(x-3)=12/(3-x)(3+x)

4x/(x+3)-x/(x-3)=-12/(x-3)(x+3)

Numitorul comun e (x-3)(x+3).

4x(x-3)-x(x+3)=-12

4x^2-12x-x^2-3x=-12

3x^2-15x=-12

3x(x-5)=-12

x(x-5)=-4

x^2-5x+4=0

x^2-x-4x+4=0

x(x-1)-4(x-1)=0

(x-1)(x-4)=0

x-1=0=>x1=1

x-4=0=>x2=4

S={1, 4}

9-x^2=3^2-x^2=(3-x)(3+x)