If I have a function that has a denominator, can i multiply it out to get rid of it

eg (x/3) + 2x + 5x = f(x)

Can i just multiply everything out by 3 so i get
x + 6x + 15x = F(x)

or will this screw up me finding critical points/intervals of increase decrease etc

Yes, but f(x) doesn't become F(x). f(x) becomes 3f(x).
x/3 + 2x + 5x = f(x)
3(x/3 + 2x + 5x) = 3(f(x))
x + 6x + 15x = 3f(x)