Bài 3:
a) \(VT=\left[\sqrt{15}+\dfrac{-\sqrt{7}\left(2-\sqrt{7}\right)}{2-\sqrt{7}}\right]\left[\dfrac{\sqrt{15}\left(\sqrt{15}-1\right)}{\sqrt{15}-1}+\sqrt{7}\right]\)
\(=\left(\sqrt{15}-\sqrt{7}\right)\left(\sqrt{15}+\sqrt{7}\right)=15-7=8=VP\)
b) \(VT=\left[2+\dfrac{\sqrt{x}\left(\sqrt{y}+1\right)}{\sqrt{y}+1}\right]\left[2-\dfrac{\sqrt{x}\left(\sqrt{y}-1\right)}{\sqrt{y}-1}\right]\)
\(=\left(2+\sqrt{x}\right)\left(2-\sqrt{x}\right)=4-x=VP\)
Bài 4:
a) ĐKXĐ: \(x\ge-1\)
\(pt\Leftrightarrow2\sqrt{x+1}+3\sqrt{x+1}-4\sqrt{x+1}=4\)
\(\Leftrightarrow\sqrt{x+1}=4\Leftrightarrow x+1=16\Leftrightarrow x=15\left(tm\right)\)
b) ĐKXĐ: \(x\ge5\)
\(pt\Leftrightarrow2\sqrt{x-5}-\sqrt{x-5}+\sqrt{x-5}=2\)
\(\Leftrightarrow2\sqrt{x-5}=2\Leftrightarrow\sqrt{x-5}=1\Leftrightarrow x-5=1\Leftrightarrow x=6\left(tm\right)\)
Bài 5:
a) ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\x\ne1\end{matrix}\right.\)
\(A=\dfrac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}-1}+\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}=\sqrt{x}-1+\sqrt{x}=2\sqrt{x}-1\)
b) \(A=2\sqrt{x}-1< 1\Leftrightarrow2\sqrt{x}< 2\Leftrightarrow\sqrt{x}< 1\Leftrightarrow x< 1\)
Kết hợp ĐKXĐ:
\(\Leftrightarrow0\le x< 1\)
Bài 6:
a) \(D=\dfrac{1+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}+1}{\sqrt{x}\left(x-2\sqrt{x}+1\right)}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}\left(\sqrt{x}-1\right)}.\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)^2}{\sqrt{x}+1}=\sqrt{x}-1\)
b) \(D=\sqrt{x}-1=\sqrt{8-2\sqrt{7}}-1=\sqrt{\left(\sqrt{7}-1\right)^2}-1=\sqrt{7}-1-1=\sqrt{7}-2\)
