[tex] \dfrac{ \dfrac{x+3}{4x^2-16} }{ \dfrac{2x^2+10x+12}{2x-4} } [/tex]
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Write the divide fraction horizontally:
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[tex]= \dfrac{x+3}{4x^2-16} \div \dfrac{2x^2+10x+12}{2x-4} [/tex]
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Factorise the numerators and denominators when possible:
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[tex]= \dfrac{x+3}{4(x+2)(x-2)} \div \dfrac{ 2(x + 3) (x + 2)}{2(x-2)} [/tex]
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Convert the divide fraction to multiplication fraction
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[tex]= \dfrac{x+3}{4(x+2)(x-2)} \times \dfrac{2(x-2)}{2(x+3)(x+2)} [/tex]
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Cancel the factors
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[tex]= \dfrac{1}{4(x+2)} \times \dfrac{1}{(x+2)} [/tex]
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Combine to single fraction
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[tex]= \dfrac{1}{4(x+2)^2} [/tex]
