Partial fractions—The 'cover-up method'

Posted on 2006-03-22
Last Modified: 2011-09-20
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 :)
Question by:InteractiveMind
    LVL 84

    Accepted Solution

    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
    LVL 25

    Author Comment

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

    LVL 25

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