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 $0<t\le 1$, but his answer is $1-\frac{t}{4}$ regardless of $z$ when $0<t\le 1$). So I want to ask for a hint. Sorry the problem is really of low level.