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      <text>3.6.1.1 Proper and improper fractions</text>
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      <text><![CDATA[<h4>Proper and improper fractions</h4>
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<p>Frequently we find that an algebraic fraction appears in the form</p>
<p>\[\text{algebraic fraction} = {\hbox{numerator}\over \hbox{denominator}}\]
</p>
<p> where both numerator and denominator are polynomials. For example:
</p>
<p>\(\displaystyle{{x^3+x^2+3x+7\over x^2+1}; \qquad {3x^2-2x+5\over x^2-7x+2}; \qquad {x\over x^4+1}.}\)</p>
<p> The <span><strong>degree</strong></span> of the numerator, <span class="math inline">\(n\)</span> say, is the highest power occurring in the numerator. The degree of the denominator, <span class="math inline">\(d\)</span> say, is the highest power occurring
    in the denominator.&nbsp;</p>
<p>If <span class="math inline">\(d&gt;n\)</span> the fraction is said to be <span><strong>proper</strong></span>; the third expression above is such an example.&nbsp;</p>
<p>If <span class="math inline">\(d\le n\)</span> the fraction is said to be <span><strong>improper</strong></span>; the first and second expressions above are examples of this type.&nbsp;</p>
<p>Before calculating the partial fractions of an algebraic fraction it is important to decide whether the fraction is proper or improper.</p>]]></text>
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