Question

Rezolvati in Z ecuatia 1/x+1/x-1=2/x+1 (rog rezolvarea completa)

Answer 1

$x \neq \{ -1;0;1\}. \\ \\ Inmultim~ecuatia ~cu~x(x-1)(x+1): \\ (x-1)(x+1)+x(x+1)=2x(x-1) \\ x^{2} -1+ x^{2}+x= 2x^{2} -2x \\ 2 x^{2}-1+x = 2x^{2} -2x \\ 2x^{2}-2 x^{2} -1=-2x-x \\ -1=-3x \Rightarrow x= \frac{1}{3} \notin Z. \\ \\ Ecuatia ~nu~are~solutii~in~Z.$