Joint distributions where one is uniform 
Let $X$ have a uniform distribution on the interval $(0,1)$.
a) Find the c.d.f. and p.d.f. of $Y=\dfrac{X}{1-X}$.
b) Find the c.d.f. and p.d.f. of $W=\ln Y$.

I am extremely confused on part A, and part B also.  I get to this very early step and am stuck:
$$Y= \dfrac{X}{1-X} \\ \boxed{ F_Y(y)=\Pr(Y\le y)=\Pr\left(\frac{X}{1-X}\le y\right) = \Big\vert } $$
I can't figure out how to isolate for $y$ here. Any help would be appreciated.

We have 
$$F_Y(y)=\Pr(Y\le y)=\Pr\left(\frac{X}{1-X}\le y\right).$$
This is $\Pr(X\le y(1-X))$, which is $\Pr(X(1+y)\le y)$. Finally, for $y$ positive, which is the only interesting part, we have
$$F_Y(y)=\Pr\left(X\le \frac{y}{1+y}\right)=\frac{y}{1+y}.$$
Elsewhere, we have $F_Y(y)=0$.
For the density function, differentiate. 
The second problem is handled in an analogous way. Note that $W\le w$ if and only if $\ln Y\le w$ if and only if $Y\le e^w$.
