Rút gọn A = \(\left(\frac{3}{\sqrt{x}-1}-\frac{\sqrt{x}-3}{x-1}\right)\div\left(\frac{x+2}{x+\sqrt{x}-2}-\frac{\sqrt{x}}{\sqrt{x}+2}\right)\)
\(A=\left[\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3\sqrt{x}+9}{x-9}+\frac{2\sqrt{x}}{\sqrt{x}+3}\right]\div\left[\frac{2\sqrt{x}-2}{\sqrt{x}-3}-1\right]\)
a) Tìm tập xác định và rút gọn A
b) \(x=?\) để \(A< -1\)
a)ĐKXĐ:x>=0;x khác 9
A=[\(\frac{\sqrt{x}}{\sqrt{x}-3}\) - \(\frac{3\sqrt{x}+9}{x-9}\)+ \(\frac{2\sqrt{x}}{\sqrt{x}+3}\)] \(\div\) [\(\frac{2\sqrt{x}-2}{\sqrt{x}-3}\)-1]
A=[\(\frac{\sqrt{x}\left(\sqrt{x}-3\right)-3\sqrt{x}-9+2\sqrt{x}\left(\sqrt{x}-3\right)}{x-9}\)] \(\div\) [\(\frac{\left(2\sqrt{x}-2\right)\left(\sqrt{x}+3\right)-x+9}{x-9}\)]
A=[\(\frac{3x-12\sqrt{x}-9}{x-9}\)].[\(\frac{x-9}{x-4\sqrt{x}+3}\)]
A=\(\frac{3x-12\sqrt{x}-9}{x-4\sqrt{x}+3}\)
Bài 1: Rút gọn biểu thức sau
\(P=\left(\frac{1}{\sqrt{x}-\sqrt{x-1}}-\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\right)\left(\frac{2}{\sqrt{2}-\sqrt{x}}-\frac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)
Rút gọn : \(\left(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{x-\sqrt{x}}\right):\left(\frac{1}{x+\sqrt{x}}-\frac{2}{1-x}\right)\)
\(\left(\frac{\sqrt{x}}{\sqrt{x}-1}-\frac{1}{x-\sqrt{x}}\right):\left(\frac{1}{x+\sqrt{x}}-\frac{2}{1-x}\right)\) (ĐKXĐ : \(x>0;x\ne1;x\ne\frac{1}{9}\) )
\(=\left[\frac{x}{\sqrt{x}\left(\sqrt{x}-1\right)}-\frac{1}{\sqrt{x}\left(\sqrt{x}-1\right)}\right]:\left[\frac{\sqrt{x}-1}{\sqrt{x}.\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}+\frac{2\sqrt{x}}{\sqrt{x}.\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right]\)
\(=\frac{\sqrt{x}+1}{\sqrt{x}}:\frac{3\sqrt{x}-1}{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}=\frac{\sqrt{x}+1}{\sqrt{x}}.\frac{\sqrt{x}\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{3\sqrt{x}-1}\)
\(=\frac{\left(\sqrt{x}+1\right)^2\left(\sqrt{x}-1\right)}{3\sqrt{x}-1}\)
Rút gọn biểu thức: \(P=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}+3}\right)\)
\(P=\left(\frac{2\sqrt{x}}{\sqrt{x}+3}+\frac{\sqrt{x}}{\sqrt{x}-3}-\frac{3x+3}{x-9}\right):\left(\frac{2\sqrt{x}-2}{\sqrt{x}+3}\right)\)
\(=\left(\frac{2x-6\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}+\frac{x+3\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}-\frac{3x+3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}+9\right)}\right).\frac{\sqrt{x}+3}{2\left(\sqrt{x}-1\right)}\)
\(=\frac{-3\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}.\frac{\sqrt{x}+3}{2\sqrt{x}-2}=\frac{-3\sqrt{x}-3}{2x-8\sqrt{x}+6}\)
Nếu đề ko sai thì đấy là kết quả
Rút gọn : \(\left(\frac{\sqrt{x}-1}{\sqrt{x+1}}+\frac{\sqrt{x}+1}{\sqrt{x-1}}\right).\left(1-\frac{2}{x+1}\right)^2\)
Cho P = \(\left(\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{\sqrt{x}}{x-1}\right):\left(\frac{2}{x}-\frac{2-x}{x\left(\sqrt{x}+1\right)}\right)\)
a) Rút gọn P
b) Tính P với x=\(\frac{2}{2-\sqrt{3}}\)
c) Tìm giá trị nhỏ nhất của \(\sqrt{P}\)
ĐKXĐ: ...
\(P=\left(\frac{\sqrt{x}}{\sqrt{x}-1}+\frac{\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right):\left(\frac{2}{x}-\frac{2-x}{x\left(\sqrt{x}+1\right)}\right)\)
\(=\left(\frac{\sqrt{x}\left(\sqrt{x}+1\right)+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right):\left(\frac{2\left(\sqrt{x}+1\right)-2+x}{x\left(\sqrt{x}+1\right)}\right)\)
\(=\frac{\left(x+2\sqrt{x}\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}.\frac{x\left(\sqrt{x}+1\right)}{\left(x+2\sqrt{x}\right)}=\frac{x}{\sqrt{x}-1}\)
\(x=\frac{2}{2-\sqrt{3}}=\frac{4}{4-2\sqrt{3}}=\left(\frac{2}{\sqrt{3}-1}\right)^2\)
\(\Rightarrow P=\frac{\frac{2}{2-\sqrt{3}}}{\frac{2}{\sqrt{3}-1}-1}=\frac{\frac{2}{2-\sqrt{3}}}{\frac{3-\sqrt{3}}{\sqrt{3}-1}}=\frac{2}{2\sqrt{3}-3}\)
\(\sqrt{P}\) xác định khi \(x>1\)
Khi đó: \(\sqrt{P}=\sqrt{\frac{x}{\sqrt{x}-1}}=\sqrt{\frac{x}{\sqrt{x}-1}-4+4}=\sqrt{\frac{\left(\sqrt{x}-2\right)^2}{\sqrt{x}-1}+4}\ge2\)
\(\sqrt{P}_{min}=2\) khi \(x=4\)
Rút gọn: \(A=\frac{\sqrt{1+\sqrt{1-x^2}}.\left[\sqrt{\left(1+x\right)^3}-\sqrt{\left(1-x\right)^3}\right]}{2+\sqrt{1-x^2}}\)
Giải giúp mk... Mk cần gấp.
\(\left[\frac{2\sqrt{x}+x}{x\sqrt{x}-1}-\frac{1}{x\sqrt{x}-1}\right]:\left[1-\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right]\)
a, rút gọn P
b,tính Q khi x=9
c,tính Q khi x=\(\sqrt{3}+\sqrt{7-4\sqrt{3}}\)
\(F=\left(\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{\sqrt{x}+1}{\sqrt{x}-2}-\frac{2\sqrt{x}+7}{x-4}\right):\left(\frac{3-\sqrt{x}}{\sqrt{x}-2}+1\right)\)
a,rút gọn
b,tính F biết x=9-\(4\sqrt{5}\)
c, tìm GTNN của F