Răspuns:
0,5
Explicație pas cu pas:
[tex]\frac{2}{x^{2}+3x } \ +\frac{3}{x^{2}-3 x} -\frac{2x}{x^{2}-9 } =0[/tex]
[tex]\frac{2}{x(x+3)}+\frac{3}{x(x-3)} -\frac{2x}{(x-3)(x+3)} =0\\[/tex] (numitorul comun-x(x+3)(x-3) )
[tex]\frac{2(x-3)+3(x+3)-2x^{2} }{x(x-3)(x+3)}[/tex] =0 deschidem parantezele
[tex]\frac{2x-6+3x+9-2x^{2} }{x(x+3)(x-3)}[/tex] =0 calculam totul ce putem
[tex]\frac{5x+3-2x^{2} }{x(x+3)(x-3)}[/tex] =0
[tex]\frac{-2x^{2}+6x-x+3 }{x(x+3)(x-3)}[/tex]=0
[tex]\frac{-2x*(x-3)-(x-3)}{x(x+3)(x-3)}[/tex] =0
[tex]\frac{-(x-3)*(2x+1)}{x(x+3)(x-3)}[/tex] =0 simplificam (x-3)
[tex]\frac{-(2x+1)}{x(x+3)} =0[/tex]
[tex]-\frac{(2x+1)}{x(x+3)} =0[/tex] inmultim ambele parti cu -1
[tex]\frac{(2x+1)}{x(x+3)} =0[/tex] x(x+3) ducem in partea lui 0
[tex]2x+1=0[/tex]
2x=-1
x=0,5
0,5 apartine R
S=0,5
