gõ latex đi b=)

\(A=\sqrt{x}+1\) (đã thu gọn)

\(B=\dfrac{4\sqrt{x}}{x+4}\) (đã thu gọn)

\(A=x-\sqrt{x}+1=\sqrt{x}\cdot\sqrt{x}-\sqrt{x}+1=\sqrt{x}\left(\sqrt{x}-1\right)+1\)

\(A=\dfrac{3}{2\sqrt{x}}\) (đã thu gọn)

\(A=\dfrac{3}{\sqrt{x}+3}\) (đã thu gọn)

\(A=1-\sqrt{x}\) (đã thu gọn)

\(A=x-2\sqrt{x}-1=\sqrt{x}\left(\sqrt{x}-2\right)-1\)

\(a,P=\left(\dfrac{1}{\sqrt{x}-2}-\dfrac{1}{\sqrt{x}+2}\right)\cdot\left(\dfrac{\sqrt{x}+2}{2}\right)^2\left(x\ge0;x\ne4\right)\\ P=\dfrac{\sqrt{x}+2-\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{\left(\sqrt{x}+2\right)^2}{4}\\ P=\dfrac{4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{\left(\sqrt{x}+2\right)^2}{4}=\dfrac{\sqrt{x}+2}{\sqrt{x}-2}\)

\(b,\)Ta có \(x=6-2\sqrt{5}=\left(\sqrt{5}-1\right)^2\)

Thay vào \(P\), ta được:

\(P=\dfrac{\sqrt{\left(\sqrt{5}-1\right)^2}+2}{\sqrt{\left(\sqrt{5}-1\right)^2}-2}=\dfrac{\sqrt{5}-1+2}{\sqrt{5}-1-2}=\dfrac{\sqrt{5}+1}{\sqrt{5}-3}\)

\(c,\)Để \(P< 1\Leftrightarrow\dfrac{\sqrt{x}+2}{\sqrt{x}-2}< 1\)

\(\Leftrightarrow\dfrac{\sqrt{x}+2}{\sqrt{x}-2}-1< 0\\ \Leftrightarrow\dfrac{\sqrt{x}+2-\sqrt{x}+2}{\sqrt{x}-2}< 0\\ \Leftrightarrow\dfrac{4}{\sqrt{x}-2}< 0\\ \Leftrightarrow\sqrt{x}-2< 0\left(4>0\right)\\ \Leftrightarrow\sqrt{x}< 2\\ \Leftrightarrow x< 4\)

Vậy để \(P< 1\) thì \(x< 4\)

Tick nha

a: ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\x\ne4\end{matrix}\right.\)

Ta có: \(P=\left(\dfrac{1}{\sqrt{x}-2}-\dfrac{1}{\sqrt{x}+2}\right)\cdot\left(\dfrac{\sqrt{x}+2}{2}\right)^2\)

\(=\dfrac{\sqrt{x}+2-\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\dfrac{\left(\sqrt{x}+2\right)^2}{4}\)

\(=\dfrac{\sqrt{x}+2}{\sqrt{x}-2}\)

b: Thay \(x=6-2\sqrt{5}\) vào P, ta được:

\(P=\dfrac{\sqrt{5}+1+2}{\sqrt{5}+1-2}=\dfrac{3+\sqrt{5}}{\sqrt{5}+1}=\dfrac{1+\sqrt{5}}{2}\)

Ta có: \(A=\dfrac{x-4\sqrt{x}+4}{\sqrt{x}-2}+\dfrac{x+\sqrt{x}-2}{\sqrt{x}-2}\)

\(=\dfrac{2x-3\sqrt{x}+2}{\sqrt{x}-2}\)