Question

Aratati ca 2x+1 supra x-2+ 1-2x supra x+2+ x patrat+16 supra x patrat-4= x+8 supra x-2.

Answer 1

[tex] \frac{2x+1}{x-2} + \frac{1-2x}{x+2} + \frac{x^{2} +16}{ x^{2} -4} = \frac{x+8}{x-2} [/tex]
amplificam prima fractie cu x+2; a doua fractie cu x-2; iar ultima fractie cu x+2; . pentru ca numitorul celei dea treia fractie se scrie ca produs (x-2)(x+2).
iar ecuatia devine: $\frac{(2x+1)(x+2)+(x-2)(1-2x)+ x^{2} +16}{(x-2)(x+2)} = \frac{(x+8)(x+2)}{(x-2)(x+2)}$
=> $2x^{2} +4x+x+2+x-2 x^{2} -2+4x+ x^{2} +16= x^{2} +10x+16$
=> $x^{2} +10x+16= x^{2} +10x+16$