Three or more linear factors in the denominator of partial fractions

This article is a continuation from the previous article. This article explores partial fractions with three or more linear factors in the denominator. Fractions with more than two linear factors in the denominator can be split into partial fractions. We shall look at some examples below;
Expressions with three or more linear terms in the denominator such as shown below;
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…can be split into partial fractions;
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Example

In this example we shall express the following fraction into partial fractions;
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In the fraction above the denominators must be x, (x-1) and (2x+1). So we relate the fraction to the partial fraction expression as shown below;
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We can then add the fractions as we did in the previous article.
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Now we can compare the numerator to find the values of A, B, and C.
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Now we need to test a few x values to find the values of A, B, C. First we let x=1.
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Next we let x=0;
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…and lastly let x = -½
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So the expression becomes;
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