\(ĐKXĐ:x\ge0;x\ne1;x\ne4\)
\(A=\left(\dfrac{4}{\sqrt{x}-1}-\dfrac{\sqrt{x}-2}{x-3\sqrt{x}+2}\right).\left(\dfrac{\sqrt{x}-1}{x^2}\right)\)
\(=\left[\dfrac{4}{\sqrt{x}-1}-\dfrac{\sqrt{x}-2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)}\right].\left(\dfrac{\sqrt{x}-1}{x^2}\right)\)
\(=\left(\dfrac{4}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}-1}\right).\left(\dfrac{\sqrt{x}-1}{x^2}\right)\)
\(=\dfrac{3}{\sqrt{x}-1}.\left(\dfrac{\sqrt{x}-1}{x^2}\right)=\dfrac{3}{x^2}\)
A=\(\left(\dfrac{4}{\sqrt{x}-1}-\dfrac{\sqrt{x}-2}{\left(\sqrt{x}-1\right).\left(\sqrt{x}-2\right)}\right).\left(\dfrac{\sqrt{x}-1}{x^2}\right)\)
=\(\left(\dfrac{4.}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}-1}\right).\left(\dfrac{\sqrt{x}-1}{x^2}\right)\)
=\(\dfrac{4-1}{\sqrt{x}-1}.\dfrac{\sqrt{x}-1}{x^2}\)
=\(\dfrac{3.\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right).x^2}\)
=\(\dfrac{3}{x^2}\)
