I don't have a math degree.. actually, i kinda got bored with it and bailed at age 14. Either way I'm missing a piece of info for calculating some odds and would appreciate it if someone could fill the gap in my brain.

say i have a flush draw on the flop. I hit on the turn 19.14% of the time right?
ie. (9 / 47) x 100 = 19.14

if i miss the turn, i hit the river 19.56% of the time
ie. (9/46) x 100 = 19.56

so now, my uneducated brain says that i should be able to run something like this.

((9/47)x100)+((9/46)x100) = 38.71

but I know that I dont hit my flush on the turn or river 38.7% of the time, a quick gander at an outs chart says its 34.97

why is this so? is it because it allows for a runner runner hit? how would the correct equation look for calculating turn+river chances?