\(\sqrt{64-6\sqrt{7}}+\dfrac{9}{\sqrt{7}-4}+\dfrac{2\sqrt{7}-14}{\sqrt{7}-1}\\ =\sqrt{\left(3\sqrt{7}\right)^2-2\cdot3\sqrt{7}\cdot1+1^2}+\dfrac{9\left(\sqrt{7}+4\right)}{\left(\sqrt{7}-4\right)\left(\sqrt{7}+4\right)}+\dfrac{\left(2\sqrt{7}-14\right)\left(\sqrt{7}+1\right)}{\left(\sqrt{7}-1\right)\left(\sqrt{7}+1\right)}\\ =\sqrt{\left(3\sqrt{7}-1\right)^2}+\dfrac{9\left(\sqrt{7}+4\right)}{\sqrt{7}^2-4^2}+\dfrac{14+2\sqrt{7}-14\sqrt{7}-14}{\sqrt{7}^2-1^2}\\ =\left|3\sqrt{7}-1\right|-\sqrt{7}-4-\dfrac{12\sqrt{7}}{6}\\ =3\sqrt{7}-1-\sqrt{7}-4-2\sqrt{7}\\ =-5.\)
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