Repeated linear factors in the denominator of partial fractions

This article is a continuation from the previous article. This article explores partial fractions with repeated linear factors in the denominator. A fraction that has repeated linear factors in the denominator can be expressed as a partial fraction as we shall see below.
Below is an example of a linear expression with repeated linear terms in the denominator.
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The fraction above can be split into the partial fraction;
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Example

In this example we’re going to split the following fraction into partial fraction form;
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We let;
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We can now add the fractions as usual;
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Now we compare the fractions;
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Now we let x = -1 to find the value of B.
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Now we let x=-½ to find the value of C.
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To find the value of A we can equate terms in x².
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…therefore;
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…we know C=3 so we get;
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We can conclude that;
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