a) \(A=\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{\sqrt{x}}{x-1}\right):\dfrac{1}{\sqrt{x}+1}\)
\(A=\left(\dfrac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}-\dfrac{\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right)\cdot\left(\sqrt{x}+1\right)\)
\(A=\dfrac{\sqrt{x}+1-\sqrt{x}}{x-1}\cdot\left(\sqrt{x}+1\right)\)
\(A=\dfrac{1}{x-1}\cdot\left(\sqrt{x}+1\right)\)
\(A=\dfrac{\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(A=\dfrac{1}{\sqrt{x}-1}\)
Bạn nên tách ra từng câu nhé mình làm mẫu 1 câu thôi
b) \(B=\left(\dfrac{\sqrt{x}}{\sqrt{x}+2}+\dfrac{2}{\sqrt{x}-2}\right):\dfrac{x+4}{\sqrt{x}+2}\)
\(=\left(\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}+\dfrac{2\left(\sqrt{x}+2\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right).\dfrac{\sqrt{x}+2}{x+4}\)
\(=\dfrac{x-2\sqrt{x}+2\sqrt{x}+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{\sqrt{x}+2}{x+4}\)
\(=\dfrac{x+4}{\sqrt{x}-2}.\dfrac{1}{x+4}=\dfrac{1}{\sqrt{x}-2}\)
