Though, you did have a small mistake in your simplification, which was probably just a mis-type.
It should be not .
That said, we can verify that your simplification is a correct one by choosing arbitrary values for the equations, as long as we use the same values for both equations, if they put out the same answer, they are equivalent.
For this, we will make , , and
Because they both give the same answer with the same variable values, they are equivalent.