Question

cho M=\(\left(\dfrac{1}{a-\sqrt{a}}+\dfrac{1}{\sqrt{a}-1}\right).\dfrac{\sqrt{a}+1}{a-2\sqrt{a}+1}\) với 0<a\(\ne\)1

a.rút gọn M

b.so sanh M với 1

c.tìm a để M>0

Answer 1

\(a,Sửa:M=\left(\dfrac{1}{a-\sqrt{a}}+\dfrac{1}{\sqrt{a}-1}\right):\dfrac{\sqrt{a}+1}{a-2\sqrt{a}+1}\\ M=\dfrac{\sqrt{a}+1}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}=\dfrac{\sqrt{a}-1}{\sqrt{a}}\\ b,M=\dfrac{\sqrt{a}-1}{\sqrt{a}}=1-\dfrac{1}{\sqrt{a}}< 1\left(\dfrac{1}{\sqrt{a}}>0\right)\\ c,M>0\Leftrightarrow\sqrt{a}-1>0\left(\sqrt{a}>0\right)\Leftrightarrow a>1\)