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

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Answer 1 · 2015-04-07T12:14:58

$x = \frac{y - 1}{y + 1}$ $color(red)(x=(y-1)/(y+1)$

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

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

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

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

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

$x y - y = - 1 - x$ $xy-y = -1 - x$

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

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

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

$y = \frac{(1 + x)}{1 - x}$ $color(green) (y = ((1+x))/(1-x)$

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