[Rational Equations]

Solve the equation:

$$
x+\frac{x}{x}+\frac{x}{x+\frac{x}{x}}=1
$$
On the domain of definition, the equation can be reduced to $\mathrm{x}+1+\mathrm{x} /(\mathrm{x}+1)=1$. Multiply both sides of the equation by $\mathrm{x}+1$. After simplification, we get: $\mathrm{x}^{2}+2 \mathrm{x}=0$, that is, $\mathrm{x}=0$ or $\mathrm{x}=-2$. The root of the equation is only $\mathrm{x}=$ $-2$.

Answer

$-2$