# Are these two functions equivalent when y = 0?

Hello!

Am I right to conclude that:
$$y^2(A(\frac{x}{y})^2 + B(\frac{x}{y})+ C) = Ax^2 + Bxy + Cy^2$$

Only when y does not equal zero. I'm guessing I could evaluate the function lim y -> 0 but this is not the same as y explicitly equalling zero, is it? On the RHS, y can equal zero, on the LHS, y cannot equal zero. So I am guessing they are only equal when y does not equal zero.
Is this true?

Many thanks.