<s>[INST] Solve for $y$ in $x=\sqrt{(y-1)/(y+1)}$ I always struggle with this:

Express $y$ in terms of $x$ where 
  $$x = \sqrt\frac{y-1}{y+1}$$

I know to square both sides and get $x^2 = \frac{y-1}{y+1}$
Then I'm thinking multiply both sides by $y+1?$ So we get $(y+1)x^2 = y-1$
But where do I go from here? If there was only one y I would be fine.
 [/INST] Here is what I would do:
\begin{align}
x=\sqrt{\frac{y-1}{y+1}} &\Longleftrightarrow x^2 = \frac{y-1}{y+1}\\[1em]
                         &\Longleftrightarrow (y+1)x^2 = y-1\\[1em]
                         &\Longleftrightarrow yx^2+x^2=y-1\\[1em]
                         &\Longleftrightarrow yx^2-y=-(x^2+1)\\[1em]
                         &\Longleftrightarrow y(x^2-1)=-(x^2+1)\\[1em]
                         &\Longleftrightarrow y = \frac{-1}{-1}\cdot \frac{x^2+1}{1-x^2}\\[1em]
                         &\Longleftrightarrow y = \frac{x^2+1}{1-x^2}
\end{align}
Make sure you do not forget about the value restricts though (i.e., $x$ cannot be negative, $y\neq -1$, etc.). 
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