\(A=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{2x+\sqrt{x}}{\sqrt{x}}+\frac{2\left(x-1\right)}{\sqrt{x}-1}\)
\(=\frac{\sqrt{x}\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{x+\sqrt{x}+1}-\frac{2\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}}+\frac{2\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)
\(=x-\sqrt{x}-2\left(\sqrt{x}+1\right)+2\left(\sqrt{x}+1\right)\)
\(=x-\sqrt{x}\)
19.A= \(\left(\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{x}-1}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}-1}-\frac{\sqrt{x}+1}{\sqrt{x}-2}\right)\)
22.\(A=\left(\frac{x}{\sqrt{x}-1}-\sqrt{x}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}}-\frac{1}{1-\sqrt{x}}+\frac{2-x}{x-\sqrt{x}}\right)\)
12.\(A=\left(\frac{x}{\sqrt{x}-1}-\sqrt{x}\right):\left(\frac{\sqrt{x}+1}{\sqrt{x}}-\frac{1}{1-\sqrt{x}}+\frac{2-x}{x-\sqrt{x}}\right)\)
11.A=\(\left(\frac{2\sqrt{x}+1}{x\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\right):\left(\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\)
20.\(E=\left(\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}\right)+\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}+\frac{\sqrt{x}-1}{\sqrt{x}+1}\right)\)
Rút gọn biểu thức :
E=\(\frac{\sqrt{2x+2\sqrt{x^2-4}}}{\sqrt{x^2-4}+x+2}\)
F=\(\frac{\left(\frac{3}{\sqrt{1+a}}+\sqrt{1+a}\right)}{\left(\frac{3}{\sqrt{1-a^2}}+1\right)}\)
HELP ME !
1.\(\left(\frac{x+2}{x\sqrt{x}-1}+\frac{\sqrt{x}}{x+\sqrt{x}+1}+\frac{1}{1-\sqrt{x}}\right):\frac{\sqrt{x}-1}{2}\)
A=\(\left(\frac{\sqrt{x}}{\sqrt{x-1}}+\frac{\sqrt{x}}{x-1}\right):\left(\frac{2}{x}-\frac{2-x}{x\sqrt{x}+x}\right)\)
a. Rút gọn A
b. Tính A vs x=3+2\(\sqrt{2}\)
Giải phương trình :
a) \(\left(\sqrt{x}-2\right)\left(5-\sqrt{x}\right)=4-x\)
b) \(\frac{\sqrt{x+5}}{\sqrt{x+4}}=\frac{\sqrt{x-2}}{\sqrt{x+3}}\)
c) \(\frac{1}{x+\sqrt{x^2+1}}+\frac{1}{x-\sqrt{x^2+1}}=4\)
