Simplifying A Rational Expression

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The original rational expression is equal to x-2, PROVIDED x is not equal to either 0 or 3.
If we graphed y = the original expression, and we graphed y = x-2, we can see that the orginal has "holes" on the graph at (0, -2) and (3, 1), while the graph of x-2 has no holes. To make them the same, we have to exclude those two x-values for x-2.

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Alternatively use algebraic long division