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      <text>1.4.1.7 Cancelling Common Factors</text>
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      <text><![CDATA[<h4 class="HELM_example">Example</h4>
<p>Show that the algebraic fraction \(\dfrac{3}{x+1}\) and \(\dfrac{3(x+4)}{x^2+5x+4}\) are equivalent.</p>

<h4 class="HELM_solution">Solution</h4>
<p>The denominator \(x^2+5x+4\) can be factorised as \((x+4)(x+1)\) so that</p>
<p>\(\qquad \dfrac{3(x+4)}{x^2+5x+4} = \dfrac{3(x+4)}{(x+4)(x+1)}\)</p>
<p>Note that \((x + 4)\) is a factor common to both the numerator and the denominator and can be cancelled to leave \(\dfrac{3}{x+1}\). Thus \(\dfrac{3}{x+1}\) and \(\dfrac{3(x+4)}{x^2+5x+4}\) are equivalent fractions</p>]]></text>
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