Partial fractions—The 'cover-up method'

For anyone who needs a quick bit of revising, see:
for an example of the cover-up method.

Now, I've remembered pretty much everything I need to do, and for all fractions with distinct linear factors, I can use this technique to solve a partial fractions problem.

However, I don't understand how it actually works ...

For example, one of the steps requires that for each factor, you set x to a value that cancels one of the factors out. But by doing this, it sets that factor to be equal to 0 ... which surely should result in the entire denominator being 0 .......

How can this be?

Please explain. Thanks :)
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Consider it the limit as the denominator of the factor approaches 0.
the term approaches infinity and becomes the domimant term so you can ignore the others
the ratio of the term to the entire fraction is then approaches the factor for that term

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InteractiveMindAuthor Commented:
I guess that's an easy way of thinking of it :)

InteractiveMindAuthor Commented:
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