Question

19.A= \(\left(\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{x}-1}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}-1}-\frac{\sqrt{x}+1}{\sqrt{x}-2}\right)\)

Answer 1

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

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

\(A=\left(\frac{\sqrt{x}-1}{x-\sqrt{x}}-\frac{\sqrt{x}}{x-\sqrt{x}}\right):\left(\frac{x-4}{x-2\sqrt{x}-\sqrt{x}+2}-\frac{x-1}{x-\sqrt{x}-2\sqrt{x}+2}\right)\)

\(A=\left(\frac{\sqrt{x}-1-\sqrt{x}}{x-\sqrt{x}}\right):\left(\frac{x-4-x+1}{x-3\sqrt{x}+2}\right)\)

\(A=\left(\frac{-1}{x-\sqrt{x}}\right):\left(\frac{-3}{2-2\sqrt{x}}\right)\)

\(A=\frac{-1\left(2-2\sqrt{x}\right)}{-3\left(x-\sqrt{x}\right)}=\frac{2\sqrt{x}-2}{3\sqrt{x}-3x}\)

Xog trục căn thức ở mẫu....

Answer 2

\(A=\left(\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{x}-1}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}-1}-\frac{\sqrt{x}+1}{\sqrt{x}-2}\right)\)(ĐKXĐ: \(\left\{{}\begin{matrix}x\ge0\\x\ne1\\x\ne4\end{matrix}\right.\))

\(=\frac{\sqrt{x}-1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}:\frac{x-2-x+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\)

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

\(=\frac{\sqrt{x}-2}{\sqrt{x}}\)