I have a nested feedback loop that looks like this. There is an input $X(s)$, output $Y(s)$ and a plant with a function of $$F(s)=\frac{R^3+R^2sL}{s^2R^2L-R^3s}$$
The input $X(s)$ will subtract the output $Y(s)$, and the result $X1=X(s)-Y(s)$ will be multiplied by the plant function above into $X2=F(s) \cdot X1$, then $X2$ will add $X$ to get $Y$ ($X2+X(s)=Y(s)$). I can't see where I can move things left or right to "unnest" them. Could you guys help me?
Let us write $$\begin{aligned}X_1(s) &= X(s) - Y(s) \\ X_2(s) &= F(s)X_1(s) = F(s)X(s) - F(s)Y(s) \\ Y(s) &= X(s) + X_2(s) \\&= X(s) + F(s)X(s) - F(s)Y(s)\end{aligned}.$$ Then $$ \left(1+F(s)\right)Y(s) = \left(1+F(s)\right)X(s) $$ and $Y(s) = X(s)$.