Hey petenice.

The reason why they multiply it is because they want to get it into the form of x^5/y^3 which is equal to 1 by the definition of the initial relationship so it cancels.

For your second question, this is just the normal quotient rule where d/dx(u/v) = [vu' - uv']/v^2.

u = 5y, v = 3x, u' = 5y', u' = 3 so [vu' - uv']/v^2 = [(3x)(5y') - (5y)(3)]/(9x^2) because y' = dy/dx and d/dx(3x) = 3.