You titled this "transpose"' so I assume that by "defining x" you mean you want to solve the equation for x- get "x= ...". You have the equation Now what exactly is the equation? would interpret what you have as "\(\displaystyle y= \left(1- \frac{2x}{1- x}\right)^{1/2}\). Am I correct that the "0.5" on the right is a power (square root) rather than just multiplied? If that is correct then you start by undoing the square root by squaring both sides: \(\displaystyle y^2= 1- \frac{2x}{1- x}\(\displaystyle . Then \(\displaystyle \frac{2x}{1- x}= 1- y^2\). Now get rid of that fraction by multiplying \(\displaystyle 2x= (1- y^2)(1- x)= (1- y^2)- x(1- y^2)\). Now get x on the left only by adding \(\displaystyle x(1- y^2)\) to both sides: \(\displaystyle 2x+ x(1- y^2= x(3- y^2)= 1- y^2\). The last step, of course, is to get rid of that "\(\displaystyle 3- y^2\) on the left by dividing both sides by \(\displaystyle 3- y^2\).\)\)
