Is there a solution of $(x-1)/x=1$ or $(x+1)/x=1$?

Question

Is there a solution of $(x-1)/x=1$ or $(x+1)/x=1$?

Layman is trying to reversing golden ratio. Tell a real solution and complex solution please. Intuition says there should be a real value of $x$.

Answer 1

Both equations are equivalent to $0=1$, so there are no solutions. To see that, first multiply with $x$ on both sides, then substract $x$ on both sides.

Answer 2

Note that $$\frac{x-1}x=1-\frac1x$$ and $$\frac{x+1}x=1+\frac1x\;;$$ since $\dfrac1x$ is never $0$, neither of these can be equal to $1$ for any value of $x$.

Answer 3

Hint: The equation that gives the golden ratio for x is $\frac{x+1}{x}=x$