$\Big(\frac{x+5\sqrt{x}-27}{x-16}+\frac{3-\sqrt{x}}{\sqrt{x}-4}\Big):\frac{1}{\sqrt{x}+4}$
$(ĐK: x\ne16; x≥0)$
$=\Big(\frac{x+5\sqrt{x}-27}{(\sqrt{x}-4)(\sqrt{x}+4)}+\frac{3-\sqrt{x}}{\sqrt{x}-4}\Big):\frac{1}{\sqrt{x}+4}$
$=\frac{x+5\sqrt{x}-27+(3-\sqrt{x})(\sqrt{x}+4)}{(\sqrt{x}-4)(\sqrt{x}+4)}:\frac{1}{\sqrt{x}+4}$
$=\frac{x+5\sqrt{x}-27+3\sqrt{x}+12-x-4\sqrt{x}}{(\sqrt{x}-4)(\sqrt{x}+4)}.(\sqrt{x}+4)$
$=\frac{4\sqrt{x}-15}{\sqrt{x}-4}$