I've been doing some calculations in fractions, and found this equation pop up to calculate my answer:
$$\frac{1-x}{1+x}=x$$
the initial equation is
$$\frac{2(x-1)}{\frac{4(x+1)}{2}}+x=4x+9(-4x-2)-2(-17x+34)+61+6$$
(I used a random number generator)I started tackling it by solving the right side
$$ \begin{align} \cdots&=4x+9(-4x+2)-2(-17x+34)+61+6\\ &=4x+(-36x)+18-(-34x)-68+61+6\\ &=4x+(-36x)+18-(-34x)-68+61+6\\ &=4x-36x+1+34x-68+61+6\\ &=2x\\ \end{align} $$
then i simplified it even further using the other side as well, getting:
$$ \begin{align} \frac{2(x-1)}{\frac{4(x+1)}{2}}+x&=2x\\ \frac{2(x-1)}{2(x+1)}+x&=2x\\ \frac{x-1}{x+1}+x&=2x\\ \frac{x-1}{x+1}&=x\\ \end{align} $$
This is my problem. so what is $x???$ also, did I do this correctly? if not, could you solve the equation for me, and then still solve this annoying equation?