<s>[INST] Rationalise the denominator and simplify $\frac {3\sqrt 2-4}{3\sqrt2+4}$ Does someone have an idea how to work $\dfrac {3 \sqrt 2 - 4} {3 \sqrt 2 + 4}$ by rationalising the denominator method and simplifying?
 [/INST] $\dfrac{3\sqrt 2 - 4}{3\sqrt 2 + 4} \cdot \dfrac{3\sqrt 2 - 4}{3\sqrt 2 - 4}=$

 $=\dfrac{18-24\sqrt 2 + 16}{(3\sqrt 2)^2-4^2}=\dfrac{34-24\sqrt 2}{18-16}=\dfrac{2(17-12\sqrt 2)}{2}=$

$=17-12\sqrt 2.$
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