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      <text>1.4.2.3 Mult and div of algebraic fractions - examples</text>
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<h4 class="HELM_example">Example</h4>
<p>Simplify: \( \dfrac{\dfrac{2x}{y}}{\dfrac{3x}{2y}}\)</p>

<h4 class="HELM_solution">Solution</h4>
<p>We can write the fraction as \(\dfrac{2x}{y} \div \dfrac{3x}{2y}.\)</p>
<p>Inverting the second fraction and multiplying we find:</p>
<p>\[\dfrac{2x}{y} \times \dfrac{2y}{3x} = \dfrac{4xy}{3xy} = \dfrac{4}{3}\]</p>


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<h4 class="HELM_example">Example</h4>
<p>Simplify: \[ \dfrac{4x+2}{x^2+4x+3} \times \dfrac{x+3}{7x+5} \]</p>

<h4 class="HELM_solution">Solution</h4>
<p>Factorising the numerator and denominator we find</p>
<p>\[\dfrac{4x+2}{x^2+4x+3} \times \dfrac{x+3}{7x+5} = \dfrac{2(2x+1)}{(x+1)(x+3)} \times \dfrac{x+3}{7x+5}\]</p><p>\[ = \dfrac{2(2x+1)(x+3)}{(x+1)(x+3)(7x+5)}\] </p>
<p> \[= \dfrac{2(2x+1)}{(x+1)(7x+5)}\]</p>]]></text>
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