Transformation of random variables with exponential distribution

I am wondering about the distribution of 2 random variable with exponential distribution. The transformation cases are: W=X/(X+Y) and Z=(X-Y)/(X+Y) where Y and X distribute exponential distribution with lambda parameter.

Can someone help me for these transformation?

Moreover, i am also doing conditional transformation z: X|(X+Y)~Hypergeometric(m+n, n; z) where X~Bin(n,p) and Y~Bin(m, p) but i did not get the hypergeometric distribution. Seems like i did something wrong. I just simply used conditional probability theorem which is P(X|X+Y) = P(X, X+Y)/P(X+Y). Can i estimate this way? or am i wrong?