Question

$\frac{1}{x-1} = \frac{x-1}{1}$

pentru x e R \ {1} rezolva ecuatia de mai sus

Answer 1

[tex]\dfrac{1}{x-1}=\dfrac{x-1}{1}\\ \text{Inmultind pe diagonala obtinem:}\\ (x-1)^2=1\\ |x-1|=1\\ \rightarrow x-1=1\Rightarrow x_1=2\\ \rightarrow x-1=-1\Rightarrow x_2=0\\ S:x\in \{0;2\}[/tex]