TITLE: How to find value of $x$ in this formula
QUESTION [1 upvotes]: I have this formula:
$$1-\frac 1x=y$$
How do I invert this so that, if I have value of $y$, I want to find value of $x$.
I know, but I am pretty dense in math :(
I dont even know what category to put this under! Any help is appreciated!

REPLY [4 votes]: \begin{align}
1 - \frac{1}{x} &= y \\
1 &= \frac{1}{x} + y \\
1 - y &= \frac{1}{x} \\
x &= \frac{1}{1-y}
\end{align}
If $y = 1$, the above solution is undefined because there is no $x$ such that $1 - \frac{1}{x} = y$ because we would have
\begin{align}
1 - \frac{1}{x} &= 1 \\
\frac{1}{x} &= 0 \\
\end{align}
which is undefined (looking at a graph of $f(x) = \frac{1}{x}$ is another way to see this).

REPLY [1 votes]: First write as $1-y=\frac1x$.  Then reciprocate $\frac{1}{1-y}=x$
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