Question

Пж все подробно,даю 50 баллов​

Answer 1

$\displaystyle\bf\\1)\\\\\frac{\sqrt{a}+1 }{\sqrt{a} -1} -\frac{\sqrt{a} -1}{\sqrt{a}+1 } +4\sqrt{a} =\frac{(\sqrt{a} +1)\cdot(\sqrt{a} +1)-(\sqrt{a} -1)\cdot(\sqrt{a}-1) }{(\sqrt{a} -1)\cdot(\sqrt{a} +1)} +4\sqrt{a} } =\\\\\\=\frac{a+2\sqrt{a} +1-a+2\sqrt{a} -1}{a-1} +4\sqrt{a} =\frac{4\sqrt{a} }{a-1} +4\sqrt{a} \\\\\\2)\\\\\\sqrt{\frac{a}{4} } -\frac{1} {\sqrt{4a} } =\frac{\sqrt{a} }{2} -\frac{1}{2\sqrt{a} } =\frac{\sqrt{a}\cdot\sqrt{a} -1}{2\sqrt{a} } =\frac{a-1}{2\sqrt{a} }$

$\displaystyle\bf\\3)\\\\\Big(\frac{4\sqrt{a} }{a-1} +4\sqrt{a} \Big)\cdot\Big(\frac{a-1}{2\sqrt{a}} \Big)=\frac{4\sqrt{a} }{a-1} \cdot\frac{a-1}{2\sqrt{a}} +4\sqrt{a} \cdot\frac{a-1}{2\sqrt{a} } =\\\\\\=2+2\cdot(a-1)=2+2a-2=2a$