When simplifying the rational expression, explain why it is improper to cancel out the x's. State a general rule for canceling factors in a rational expression and give an example of how this rule would be used?

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Rhiannon Allan Profile
Rhiannon Allan answered
If you have to find out what the value of x is, then you need to keep the x in order for it to end up equalling to something else
Oddman Profile
Oddman answered
Whether it is improper or not depends on the context. If you are simplifying something of the nature of
it might be completely appropriate to cancel the x terms. On the other hand, you should recognize that the function will be undefined at x=0 as well as being undefined at x=2. Even though the function is undefined at x=0, it can still be differentiated and integrated across that point. (The limit exists at that point, so the expression is not indeterminate.) Here is a plot of it. It is identical to the plot of (x-3)/(x-2).

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