How do you solve $x=(y-1)/(y+1)$ for y?

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Answer 1 · 2015-04-07T12:14:58

$color(red)(x=(y-1)/(y+1)$

Multiplying both sides of the equation with $y+1$ will give us

$x*(y+1) = y-1$

Using the Distributive property $a*(b+c) = a*b + a*c$ on the left hand side, we get

$x*y + x = y -1$

Transposing $y$ to the Left Hand Side and $x$ to the Right Hand Side, we get

$xy-y = -1 - x$

$y*(x-1) = -(1+x)$

$y = (-(1+x))/(x-1)$

$y = ((1+x))/-(x-1)$

$color(green) (y = ((1+x))/(1-x)$

How do you solve x=(y-1)/(y+1)x=(y-1)/(y+1) for y?