Use the quadratic to solve for x:
x-1 = 2x+1
2-x
Please show all working out, thanks.
Which part are you having trouble with?
First you need to rearrange the equation into the form $\displaystyle ax^2+bx+c=0$
so you have:
$\displaystyle \frac{x-1}{2-x}=2x+1$
$\displaystyle x-1=\left ( 2x+1\right )\left ( 2-x\right )$
$\displaystyle x-1=4x-2x^2+2-x$
$\displaystyle 2x^2-2x-3=0$
So now you can see that $\displaystyle a=2$, $\displaystyle b=-2$ and $\displaystyle c=-3$
Once you plug these values into to quadratic formula and simplify it, you will have the solutions. Are you ok with this part?