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

Apr 7, 2015

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

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

$x \cdot \left(y + 1\right) = y - 1$

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

$x \cdot y + x = y - 1$

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

$x y - y = - 1 - x$

$y \cdot \left(x - 1\right) = - \left(1 + x\right)$

$y = \frac{- \left(1 + x\right)}{x - 1}$

$y = \frac{\left(1 + x\right)}{-} \left(x - 1\right)$

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