Hình như đề sai ! Sửa :
\(\left(\frac{1}{\sqrt{x+1}}-\sqrt{1-x}\right):\left(\frac{1}{\sqrt{1-x^2}}-1\right)\)
\(=\frac{1-\sqrt{1-x^2}}{\sqrt{1+x}}:\frac{1-\sqrt{1-x^2}}{\sqrt{1-x^2}}\)
\(=\frac{\left(1-\sqrt{1-x^2}\right)\left(\sqrt{1-x^2}\right)}{\left(\sqrt{1+x}\right)\left(1-\sqrt{1-x^2}\right)}\)
\(=\sqrt{1-x}\)
1. Rút gọn
P=\(2\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}:\left[\sqrt{1+\frac{1}{4}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2}-\frac{1}{2}\left(\sqrt{\frac{1}{x}}-\sqrt{x}\right)^2\right]\)
RG
A = \(\left(\frac{1}{x-\sqrt{x}}+\frac{1}{\sqrt{x}-1}\right):\frac{\sqrt{x}+1}{x-2\sqrt{x}+1}\)
B = \(\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right).\left(\frac{1-x}{\sqrt{2}}\right)^2\)
Rút gọn A = \(1-\left(\frac{2x-1+\sqrt{x}}{1-x}+\frac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right).\left(\frac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\right)\)
Rút gọn: \(P=1-\left(\frac{2x-1+\sqrt{x}}{1-x}+\frac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right).\frac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\)
P=\(\left(\frac{1}{\sqrt{x}-1}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}-2}-\frac{\sqrt{x}+2}{\sqrt{x}-1}\right)\)
\(\left(\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{1}{\sqrt{x}-x}\right):\left(\frac{1}{\sqrt{x}+1}-\frac{2}{1-\sqrt{x}}\right)\)
Gpt: a) \(\sqrt[4]{3\left(x+5\right)}-\sqrt[4]{11-x}=\sqrt[4]{13+x}-\sqrt[4]{3\left(3-x\right)}\)
b) \(\frac{1+2\sqrt{x}-x\sqrt{x}}{3-x-\sqrt{2-x}}=2\left(\frac{1+x\sqrt{x}}{1+x}\right)\) c) \(\sqrt{x+1}+\frac{4\left(\sqrt{x+1}+\sqrt{x-2}\right)}{3\left(\sqrt{x-2}+1\right)^2}=3\)
d) \(\sqrt{\frac{x-2}{x+1}}+\frac{x+2}{\left(\sqrt{x+2}+\sqrt{x-2}\right)^2}=1\) e) \(2x+1+x\sqrt{x^2+2}+\left(x+1\right)\sqrt{x^2+2x+2}=0\)
f) \(\sqrt{2x+3}\cdot\sqrt[3]{x+5}=x^2+x-6\)
\(B=\left(\frac{\left(x-2\right)}{x+2\sqrt{x}}+\frac{1}{\sqrt{x}+2}\right).\frac{\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\) rut gon
\(\left(\frac{1}{\sqrt{x-1}}+\frac{\sqrt{x}}{\sqrt{x-1}}\right):\frac{\sqrt{x+1}}{\left(\sqrt{x-1}\right)^2}\)
Cho biểu thức A= \(\left(\frac{1}{\sqrt{x-1}}-\frac{1}{\sqrt{x}}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x-2}}-\frac{\sqrt{x}+2}{\sqrt{x}-1}\right)\)
