\(A=\left(\dfrac{\sqrt{x}-1}{x-4}-\dfrac{\sqrt{x}}{x+4\sqrt{x}+4}\right):\dfrac{x\sqrt{x}}{\left(4-x\right)^2}\) \(\Leftrightarrow\left\{{}\begin{matrix}x\in\left(0;4\right)U\left(4;+\infty\right)\\A=\left(\dfrac{\sqrt{x}-1}{x-4}-\dfrac{\sqrt{x}}{x+4x+4}\right).\dfrac{\left(x-4\right)^2}{x\sqrt{x}}\end{matrix}\right.\)
\(A=\dfrac{\sqrt{x}-1}{x-4}.\dfrac{\left(x-4\right)^2}{x\sqrt{x}}-\dfrac{\sqrt{x}}{\left(\sqrt{x}+2\right)^2}.\dfrac{\left[\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)\right]^2}{x\sqrt{x}}\)
\(A=\dfrac{\left(\sqrt{x}-1\right)\left(x-4\right)}{x\sqrt{x}}-\dfrac{\sqrt{x}\left(\sqrt{x}-2\right)^2}{x\sqrt{x}}\\ \)
\(A=\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)-\sqrt{x}\left(\sqrt{x}-2\right)^2}{x\sqrt{x}}\\ \)
\(A=\dfrac{\left(\sqrt{x}-2\right)\left[\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)-\sqrt{x}\left(\sqrt{x}-2\right)\right]}{x\sqrt{x}}\\ \)
\(A=\dfrac{\left(\sqrt{x}-2\right)\left(3\sqrt{x}-2\right)}{x\sqrt{x}}=\dfrac{3x-8\sqrt{x}+4}{x\sqrt{x}}\)
\(\left\{{}\begin{matrix}x>0;x\ne4\\A=\dfrac{3}{\sqrt{x}}-\dfrac{8}{x}+\dfrac{4}{x\sqrt{x}}\end{matrix}\right.\)
ĐKXĐ: x ≠ 4
A = \(\left(\dfrac{\sqrt{x}-1}{x-4}-\dfrac{\sqrt{x}}{x+4\sqrt{x}+4}\right):\dfrac{x\sqrt{x}}{\left(4-x\right)^2}\)
= \(\left(\dfrac{\sqrt{x}-1}{x-4}-\dfrac{\sqrt{x}}{\left(\sqrt{x}+2\right)^2}\right).\dfrac{\left(x-4\right)^2}{x\sqrt{x}}\)
= \(\left(\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)-\sqrt{x}\left(\sqrt{x}-2\right)}{\left(x-4\right)\left(\sqrt{x}+2\right)}\right).\dfrac{\left(x-4\right)^2}{x\sqrt{x}}\)
= \(\dfrac{3\sqrt{x}-2}{\left(x-4\right)\left(\sqrt{x}+2\right)}.\dfrac{\left(x-4\right)^2}{x\sqrt{x}}\)
= \(\dfrac{\left(3\sqrt{x}-2\right)\left(\sqrt{x}-2\right)}{x\sqrt{x}}\) = \(\dfrac{3x-8\sqrt{x}+4}{x\sqrt{x}}\)
