That is true, if we talk about x = (d – b)/(a – c), but would it be true if we considered the previous step x(a – c) = d – b ? Here, a – c can be 0. If we want to divide by it, we need to consider the case a – c = 0 separately. If a – c = 0, then 0 = d – b and the equality, 0 × x = 0, holds true for any x. That's exactly what we need, because the equality must be true for any value of x, while x = (d – b)/(a – c) gives us a constant instead of a variable, which can be any number, (of course, if a - c would not be 0).
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