Flipping variables in function I'm in a bit of dilemma. I have the following formula $$ F_{b} = \frac{R_{b} - R_{0}}{R_{b} + R_{0}} $$
Variable $ F_{b} $ and $ R_{0} $ are known to me how can i pull $ R_{b} $ out so i can calculate it. If I just multiply it then I solve nothing as then I get $R_{b}$ on both sides.
 A: Start from 
$$ F_{b} = \frac{R_{b} - R_{0}}{R_{b} + R_{0}}. $$
Multiply through by $R_b+R_0$. We get
$$F_b(R_b+R_0)=R_b-R_0.$$
Multiply through on the left. We get
$$F_bR_b+F_bR_0=R_b-R_0.$$
Bring all the $R_b$ stuff to one side, the rest to the other side. (This is the key step.) We get
$$F_bR_b-R_b=-(F_bR_0+R_0)$$
Too many minus signs! Let's multiply through by $-1$. We get
$$R_b-F_bR_b=F_bR_0+R_0.$$
Note that the left-hand side is $R_b(1-F_b)$, and the right-hand side is $R_0(1+F_b)$. So our original equation has been rewritten as
$$R_b(1-F_b)=R_0(1+F_b).$$
Divide through by $1-F_b$. Of course this cannot be done if $F_b=1$. We get
$$R_b=R_0\frac{1+F_b}{1-F_b}.$$ 
Remark: We broke down the calculation into many small steps. That may have the effect of making things more complicated than they are. The actual work  is quite quick, and virtually (with a little practice) automatic.  
Your problem has a quite special form, and for that form there is a nicer way of doing things. But I wanted to use only general-purpose tools. 
A: Alternative suggestion to Andre's.  Write the RHS as:
$$ \dfrac{R_b - R_0}{R_b + R_0} = 1 - \dfrac{2 R_0}{R_b + R_0}$$
Now solve for $R_b$ as you would solve for anything before
