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I see

It just seems so enticing because the x's would cancel out (to 1?)

try and factor out x off one of the numerators or denominators (e.g. x + 3), its impossible right, so you will never get rid of x from the whole fraction

But take this example:

(x+2)/(x+7)

x and x cancel out, x/x = 1

= (1+2)/(1+7)

= 3/8

Am I misunderstanding something? It seems logical

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