Converting improper fractions into partial fractions

This article is a continuation from the previous article. I highly recommend reading through it before attempting this. This article explores how to convert improper fractions into partial fractions.
We can split improper fractions into partial fractions by dividing the numerator by the denominator. An algebraic fraction is improper when the degree of the numerator is equal to or larger than the degree of the denominator. An improper fraction must be divided first to obtain a number and a proper fraction before it can be expressed in partial fractions as we will see below.
Below are some examples of improper fractions.
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We shall look at an example below.

Example

In this example we’re going to express the following improper fraction into partial fractions.
First we shall expand the fraction;
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Now we divide as usual by dividing the denominator into the numerator;
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This article will be useful here. It offers a good explanation about how to divide partial fractions.
That must mean that;
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We can factorise the denominator to get;
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We can turn the fraction expression above into partial fractions. We let;
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We compare the numerators to find the values of A and B. Like this;
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To find the value of B we let x=2.
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To find the values of A we let x=1;
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That must mean that;
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