The problem reads find the inverse of f(x)= 2/y-3

I have the solutions manual and it says to multiply both sides by y-3 to clear the fraction. However, I find this to be too much work. I prefer to take both sides to the -1 power. Is this okay? I get the same answer which is f^-1(x)= 2/x + 3.

I just find the other method to be too much work and this method to be easier, faster and cleaner.