2/x = x/x +1
2 = x + x
2 = 2x
2x = 2
x = 2 : 2
x = 1.
\(\dfrac{2}{x}=\dfrac{x}{x+1}ĐKXĐ:x\ne-1;0\)
\(⇔ 2 ( x + 1 ) = x . x\)
\(⇔ x ^2 = 2 x + 2\)
\(⇔ x ^2 − 2 x − 2 = 0\)
\(⇔ x ^2 − 2 x + 1 − 3 = 0\)
\(\text{⇔}\left(x-1\right)^2-\sqrt{3^2}=0\)
\(\text{⇔}\left(x-1-\sqrt{3}\right)\left(x-1+\sqrt{3}\right)=0\)
\(\text{⇔}\left[{}\begin{matrix}x-1-\sqrt{3}=0\\x-1+\sqrt{3}=0\end{matrix}\right.\)
\(\text{⇔}\left[{}\begin{matrix}x=1+\sqrt{3\left(TM\right)}\\x=1-\sqrt{3}\left(TM\right)\end{matrix}\right.\)
Vậy \(S=\left\{1+\sqrt{3};1-\sqrt{3}\right\}\)
