How is y solved for in this equation?
$\displaystyle x=\frac{1-\sqrt{y}}{1+\sqrt{y}}$
$\displaystyle x=\frac{1-\sqrt{y}}{1+\sqrt{y}}$
synthetically divide:
$\displaystyle x = \frac{2}{\sqrt{y}+1} - 1$
add 1:
$\displaystyle x + 1= \frac{2}{\sqrt{y}+1}$
multiply by that denominator and divide by x+1:
$\displaystyle \sqrt{y} + 1 = \frac{2}{x + 1}$
subtract 1:
$\displaystyle \sqrt{y} = \frac{2}{x + 1} - 1$
find common denominator and add:
$\displaystyle \sqrt{y} = \frac{-x + 1}{x+1}$
square both sides:
$\displaystyle y = \frac{(-x+1)^2}{(x+1)^2}$
factor out -1 from numerator:
$\displaystyle y = \frac{(-[x-1])^2}{(x+1)^2}$
distribute ^2:
$\displaystyle y = (-1)^2\frac{(x-1)^2}{(x+1)^2}$
-1*-1 = 1:
$\displaystyle y = \frac{(x-1)^2}{(x+1)^2}$