cho biểu thức :
A=\(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{3\sqrt{x}+1}{x-1}\)
a)Nêu điều kiện và rút gọn A
b)tính A khi x=3-\(\sqrt{2}\)
c)tìm x để A=\(\dfrac{1}{2}\)
d)tìm x để A<\(\dfrac{3}{4}\)
e)tìm x nguyên để A nguyên
g)tìm x để A nguyên
h)tìm x để A min. Tìm giá trị của A khi đó
k)tìm số m để pt m.A=\(\sqrt{x}\)-2 có 2 nghiệm
l)tìm m để pt m.A=\(\sqrt{x}\)-2
a) đk:\(\left\{{}\begin{matrix}\left\{{}\begin{matrix}\sqrt{x}-1\ne0\\\sqrt{x}+1\ne0\end{matrix}\right.\\x-1\ne0\\\Rightarrow x\ne1\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}y=\sqrt{x}\Rightarrow y>0;y\ne1\\A=\dfrac{\left(y+1\right)^{^2}-\left(y-1\right)^2}{y^2-1}-\dfrac{3y+1}{y^2-1}\end{matrix}\right.\)
\(A=\dfrac{+4y-\left(3y+1\right)}{y^2-1}=\dfrac{y-1}{\left(y-1\right)\left(y+1\right)}=\dfrac{1}{y+1}=\dfrac{1}{\sqrt{x}+1}\)
\(A\left(3-\sqrt{2}\right)=\dfrac{1}{\sqrt{3-\sqrt{2}}+1}\)
c) \(\dfrac{1}{\sqrt{x}+1}=\dfrac{1}{2}\Rightarrow\sqrt{x}=1\Rightarrow x=1\left(loai\right)\) vo nghiệm
d) \(\dfrac{1}{\sqrt{x}+1}< \dfrac{3}{4}\Rightarrow3\sqrt{x}>1\Rightarrow\sqrt{x}>\dfrac{1}{3}\Rightarrow x>\dfrac{1}{9}\)
a) * Đk: \(x\ne\pm1\)
* \(A=\dfrac{\sqrt{x}+1}{\sqrt{x}-1}-\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{3\sqrt{x}-1}{x-1} \)
\(A=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}-\dfrac{3\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(A=\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}-1\right)-\left(3\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(A=\dfrac{x+\sqrt{x}+\sqrt{x}+1-x+\sqrt{x}+\sqrt{x}-1-3\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(A=\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(A=\dfrac{1}{\sqrt{x}-1}\)
c) \(A=\dfrac{1}{2}\)
\(\Leftrightarrow\dfrac{1}{\sqrt{x}-1}=\dfrac{1}{2}\)
\(\Leftrightarrow\sqrt{x}-1=2\)
\(\Leftrightarrow\sqrt{x}=3\)
\(\Leftrightarrow x=9\left(tm\right)\)
Vậy x = 9