[tex]\lim\limits_{x\to-3}\dfrac{\sqrt{x^2+7}-4\sqrt{x^2-8}}{x+3}\cdot\dfrac{\sqrt{x^2+7}+4\sqrt{x^2-8}}{\sqrt{x^2+7}+4\sqrt{x^2-8}}=\\\lim\limits_{x\to-3}\dfrac{(\sqrt{x^2+7}-4\sqrt{x^2-8})(\sqrt{x^2+7}+4\sqrt{x^2-8})}{(x+3)(\sqrt{x^2+7}+4\sqrt{x^2-8})}=\\\lim\limits_{x\to-3}\dfrac{x^2+7-16(x^2-8)}{(x+3)(\sqrt{x^2+7}+4\sqrt{x^2-8})}=\lim\limits_{x\to-3}\dfrac{x^2+7-16x^2+128}{(x+3)(\sqrt{x^2+7}+4\sqrt{x^2-8})}=[/tex]
[tex]\lim\limits_{x\to-3}\dfrac{-15x^2+135}{(x+3)(\sqrt{x^2+7}+4\sqrt{x^2-8})}=\lim\limits_{x\to-3}\dfrac{-15(x^2-9)}{(x+3)(\sqrt{x^2+7}+4\sqrt{x^2-8})}=\\\lim\limits_{x\to-3}\dfrac{-15(x-3)(x+3)}{(x+3)(\sqrt{x^2+7}+4\sqrt{x^2-8})}=\lim\limits_{x\to-3}\dfrac{-15(x-3)}{\sqrt{x^2+7}+4\sqrt{x^2-8}}=\\\dfrac{-15(-3-3)}{\sqrt{3^2+7}+4\sqrt{3^2-8}}=\dfrac{-15\cdot(-6)}{\sqrt{9+7}+4\sqrt{9-8}}=\dfrac{90}{\sqrt{16}+4\sqrt{1}}=\dfrac{90}{4+4\cdot1}=\\\dfrac{90}{4+4}=\dfrac{90}{8}=\dfrac{45}{4}=11\dfrac{1}{4}=11,25[/tex]
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