Quote:
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Originally Posted by Alan Anderson
Start with the equation a / u = (w-a) / v. You can accept multiplying both sides by u, right? You can also divide both sides by something more complicated, such as (w+b) / u. Here's the fun part: if you know that (w+b) / u = (2w-b) / v, you can divide the left side of the original equation by the left side of the new equation, while dividing the other side of the original equation by the other side of the new one. You're still dividing both sides by the same thing.
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You have to be careful that you're not dividing by zero, though. (Which would happen in the above example if w = -b or if 2w = b.) Otherwise you might convince yourself that
1 = 2. (
See my response too.)