`a)`\(A=\left(\dfrac{1}{\sqrt{x}+2}+\dfrac{7}{x-4}\right):\left(\dfrac{\sqrt{x}-1}{\sqrt{x}-2}-1\right)\)
\(A=\left(\dfrac{\sqrt{x}-2+7}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right):\left(\dfrac{\sqrt{x}-1-\sqrt{x}+2}{\sqrt{x}-2}\right)\)
\(A=\dfrac{\sqrt{x}+5}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}.\sqrt{x}-2\)
\(A=\dfrac{\sqrt{x}+5}{\sqrt{x}+2}\)
`b)`
`@`TH1:\(16x^2-625=0\)
\(\Delta=0^2-4.\left(-625\right).16=40000>0\)
`->`\(\left\{{}\begin{matrix}x=\dfrac{\sqrt{40000}}{32}=\dfrac{25}{4}\left(tm\right)\\x=\dfrac{-\sqrt{40000}}{32}=-\dfrac{25}{4}\left(ktm\right)\end{matrix}\right.\)
Thế `x=25/4` vào `A` ta được:
\(A=\dfrac{\sqrt{\dfrac{25}{4}}+5}{\sqrt{\dfrac{25}{4}}+2}=\dfrac{15}{2}:\dfrac{9}{2}=\dfrac{5}{3}\)
`@`TH2:\(x=\sqrt{27+10\sqrt{2}}-\sqrt{18+8\sqrt{2}}\)
\(x=\sqrt{\left(\sqrt{2}+5\right)^2}-\sqrt{\left(\sqrt{2}+4\right)^2}\)
\(x=\left|\sqrt{2}+5\right|-\left|\sqrt{2}+4\right|\)
\(x=\sqrt{2}+5-\sqrt{2}-4\)
\(x=1\)
Thế `x=1` vào `A` ta được:
\(A=\dfrac{\sqrt{1}+5}{\sqrt{1}+2}=\dfrac{6}{3}=2\)
