Question

rút gọn A

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

Answer 1

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

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

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

\(=\frac{x+1}{x^2-x+2\text{x}\sqrt{x}-2\sqrt{x}-1}\)

tick cho mình nha bạn