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[latex]6)\; \sqrt{x}+\sqrt{x-8}=2x-20+2\sqrt{x^2-8x}\; ,\; \; ODZ:\; x\ \textgreater \ 8\\\\(\sqrt{x}+\sqrt{x-8})^2=x+2\sqrt{x(x-8)}+x-8=2x+2\sqrt{x^2-8x}-8\; \to \\\\\sqrt{x}+\sqrt{x-8}=(\sqrt{x}+\sqrt{x-8})^2-12\\\\t=\sqrt{x}+\sqrt{x-8}}\ \textgreater \ 0\; ,\; \; t=t^2-12\; ,\\\\t^2+t-12=0\; ,\\\\ t_1=-3\ \textless \ 0\; ,\\\\ t_2=4\; \to \; \; \sqrt{x}+\sqrt{x-8}=4\\\\x+2\sqrt{x(x-8)}+x-8=16[/latex] [latex]2x+2\sqrt{x^2-8x}=24\\\\\sqrt{x^2-8x}=12-x\\\\x^2-8x=144-24x+x^2\\\\16x=144\\\\x=9[/latex] [latex]8)\; \frac{\sqrt{x+6}-\sqrt{6-x}}{\sqrt{x+6}+\sqrt{6-x}} = \frac{x}{6} \; ,\; ODZ:\; x\in (-6,6)\\\\ \frac{(\sqrt{x+6}-\sqrt{6-x})^2}{(x+6)-(6-x)} =\frac{x}{6}\\\\ \frac{x+6-2\sqrt{(x+6)(6-x)}+6-x}{2x} =\frac{x}{6}\\\\12-2\sqrt{36-x^2}=\frac{x^2}{3}\\\\2\sqrt{36-x^2}=12-\frac{x^2}{3}\\\\6\sqrt{36-x^2}=36-x^2\\\\36(36-x^2)=36^2-72x^2+x^4\\\\-36x^2=-72x^2+x^4[/latex] [latex]x^4-36x^2=0\\\\x^2(x-6)(x+6)=0\\\\x_1=0\; ,\; x_2=6\; ,\; x_3=-6\\\\x\in \varnothing[/latex]