Question

Спростити вираз
Обчисліть його значення при m = 5

Answer 1

$\displaystyle\bf\\\frac{\sqrt{m} +1}{m\sqrt{m}+m+\sqrt{m} }:\frac{1}{m^{2} -\sqrt{m}} =\\\\\\=\frac{\sqrt{m}+1 }{(\sqrt{m} )^{2}\cdot\sqrt{m} +(\sqrt{m} )^{2} +\sqrt{m} } \cdot\Big[\Big((\sqrt{m})^{2}\Big)^{2} -\sqrt{m} \Big=\\\\\\=\frac{\sqrt{m}+1 }{(\sqrt{m} )^{3}+(\sqrt{m} )^{2} +\sqrt{m} } \cdot\Big((\sqrt{m})^{4}-\sqrt{m} \Big)=\\\\\\=\frac{(\sqrt{m}+1)\cdot\sqrt{m} \cdot\Big((\sqrt{m})^{3} -1\Big) }{\sqrt{m}\cdot\Big ((\sqrt{m} )^{2}+\sqrt{m} +1\Big) }=$

$\displaystyle\bf\\=\frac{(\sqrt{m}+1) \cdot(\sqrt{m} -1)\cdot((\sqrt{m})^{2}+\sqrt{m}+1)}{\Big ((\sqrt{m} )^{2}+\sqrt{m} +1\Big) }=\\\\\\=(\sqrt{m} +1)\cdot(\sqrt{m} -1)=(\sqrt{m} )^{2} -1^{2} =m-1\\\\m=5\\\\m-1=5-1=4\\\\Otvet \ : \ 4$