Question

спростіть вираз: СРОЧНООО​

Answer 1

$\displaystyle\bf\\1)\\\\\frac{a-b}{\sqrt{a}+\sqrt{b} } =\frac{(\sqrt{a})^{2} -(\sqrt{b})^{2} }{\sqrt{a} +\sqrt{b} }=\frac{(\sqrt{a} +\sqrt{b} )\cdot(\sqrt{a} -\sqrt{b}) }{\sqrt{a} +\sqrt{b} } =\\\\\\=\sqrt{a} -\sqrt{b} \\\\2)\\\\\frac{x-\sqrt{3x} +3}{x\sqrt{x} +3\sqrt{3} } =\frac{(\sqrt{x} )^{2} -\sqrt{3x} +(\sqrt{3} )^{2} }{(\sqrt{x} )^{2} \cdot\sqrt{x} +(\sqrt{3} )^{2}\cdot \sqrt{3} } =$

$\displaystyle\bf\\=\frac{(\sqrt{x} )^{2} -\sqrt{3x} +(\sqrt{3} )^{2} }{(\sqrt{x} )^{3} +(\sqrt{3} )^{3}} =\frac{(\sqrt{x} )^{2} -\sqrt{3x} +(\sqrt{3} )^{2} }{(\sqrt{x} +\sqrt{3} )\cdot\Big((\sqrt{x} )^{2} -\sqrt{3x} +(\sqrt{3} )^{2}\Big) } =\\\\\\=\frac{1}{\sqrt{x} +\sqrt{3} }$