Transposing the equation $ y = \frac{x}{1-x} $ to get $x$

Question

I can't solve the following equation for $x$. I got my wires crossed

$ y = \frac{x}{1-x} $

Thank you very much for your help

Answer 1

we have $$y=\frac{x}{1-x}$$ ,multiplying by $1-x$ we get $$y-yx=x$$ adding $$yx$$ and we have $$y=x(1+y)$$ dividing by $$1+y\ne 0$$ we obtain $$x=\frac{y}{1+y}$$

Answer 2

$y=\frac{x}{1-x}$

$y(1-x) = x$

$y - yx = x$

$y = x + xy$

$y = x(1 + y)$

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

Interchanging two sides,

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

Answer 3

We have $$y=\frac{x}{1-x}$$ The numerator and denominator can both be divided by $x$: $$y=\frac{1}{\frac{1}{x}-1}$$ Multiplying both sides by $\frac{1}{x}-1$: $$y\left(\frac{1}{x}-1\right)=1$$ Dividing both sides by $y$: $$\frac{1}{x}-1=\frac{1}{y}$$ Can you take it from here?