Question

$\frac{2x-1}{x-2}+ \frac{1-2x}{x+2}+ \frac{ x^{2}+16 }{ x^{2} -4}$

Answer 1

[(2x-1)(x+2)+(1-2x)(x-2)+x²+16]/(x²-4)=
2x²+3x-2+x-2x²-2+4x+x²+16)/(x²-4)=
(x²+8x+12)/(x²-4)=
(x+2)(x+6)/(x-2)(x+2)=
(x+6)/(x-2)

Answer 2

1) NC = X² - 4 = ( x - 2)( x + 2), numotorul comun
2) amplifici prima fractie cu ( x + 2) si a doua fractie cu ( x - 2) ⇒
   ( 2x - 1)( x + 2) / ( x + 2)( x - 2)  +  ( 1 - -2x)( x - 2) / ( x + 2)( x - 2)  +
   + ( x² + 16) / ( x + 2)( x - 2)
  ( 2x² + 4x - x - 2) supra ( x + 2)( x - 2)  + ( x - 2 - 2x² + 4x) supra ( x+2)( x-2) + ( x² + 16) supra ( x+2)( x - 2)
  ( 2x² + 3x - 2 - 2x² + 5x - 2 + x² + 16) supra ( x+2)( x-2)
  ( x² + 8x + 12) / ( x+2)( x-2)
  ( x - 2)( x + 6) / ( x + 2)( x - 2) , se simplifica cu x - 2
   x+ 6 / x + 2
  SPER CA TI-AM FOST DE AJUTOR!