Question

cho biểu thức : M= \(^{\dfrac{a}{\sqrt{a}-1}+\dfrac{1}{\sqrt{a}+a}-\dfrac{a+1}{\sqrt{a}}}\)

a, Rút gọn M

b,Tìm a để M>2

c, Tím a để m= -1

d, Tím a \(\varepsilon\) Z để M \(\varepsilon\) Z

Answer 1

a: \(A=\dfrac{a\left(\sqrt{a}+1\right)}{a-1}+\dfrac{\sqrt{a}-1}{\sqrt{a}\left(a-1\right)}-\dfrac{a+1}{\sqrt{a}}\)

\(=\dfrac{a^2+a\sqrt{a}+\sqrt{a}-1-a^2+1}{\sqrt{a}\left(a-1\right)}\)

\(=\dfrac{a\left(\sqrt{a}+1\right)}{\sqrt{a}\left(a-1\right)}=\dfrac{\sqrt{a}}{\sqrt{a}-1}\)

b: Để M>2 thì M-2>0

\(\Leftrightarrow\dfrac{\sqrt{a}-2\sqrt{a}+2}{\sqrt{a}-1}>0\)

\(\Leftrightarrow\dfrac{\sqrt{a}-2}{\sqrt{a}-1}< 0\)

=>1<a<4

c: Để M=-1 thì \(\sqrt{a}=-\sqrt{a}+1\)

=>a=1/4