If you are careful and each step gives an equivalent statement, this is correct. For example, if you read math books/papers, whenever such transformation is made, the author usually states that it is equivalent.
However, the problem is that students apply this technique blindly manipulating the formula in any way they can/want. Such carelessness is the real problem.
However, the problem is that students apply this technique blindly manipulating the formula in any way they can/want. Such carelessness is the real problem.