What is the probability that $P(\\frac{xy}{z}\\le t)$?

What is the probability that $P(\\frac{xy}{z}\\le t)$? References This is a problem I do not know how to solve. Assume $x,y,z$ are uniformly identically distributed variables at $[0,1]$. I am supposed to calculate $$P\\left(\\frac{xy}{z}\\le t\\right)$$ I thought the computation would be similar to the case $P(xy\\le t)=t-t\\log[t]$, since we have $$P\\left(\\frac{xy}{z}\\le t\\right)=\\int \\limits^{1}_{0}P(xy\\le zt) \\, dz$$So since I do not know $zt$\'s value in principle, I can calculate it by $$\\int \\limits^{1}_{0}(zt-zt\\log[zt]) \\, dz$$ But this turned out to be very different from the answer in the solution manual, where the author distinguished cases if $t\\le 1$ or $t> 1$, and the two answers are remarkablely different(My answer only works when $0