\(\left[\frac{2\sqrt{x}+x}{x\sqrt{x}-1}-\frac{1}{x\sqrt{x}-1}\right]:\left[1-\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right]\)
a, rút gọn P
b,tính Q khi x=9
c,tính Q khi x=\(\sqrt{3}+\sqrt{7-4\sqrt{3}}\)
\(A=\left(\frac{2\sqrt{x}+x}{x\sqrt{x}-1}-\frac{1}{\sqrt{x}-1}\right):\left(\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\)
a Rút gọn biểu thức
b Tính giá trị của \(\sqrt{A}\) khi x=\(4+2\sqrt{3}\)
\(F=\left(\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{\sqrt{x}+1}{\sqrt{x}-2}-\frac{2\sqrt{x}+7}{x-4}\right):\left(\frac{3-\sqrt{x}}{\sqrt{x}-2}+1\right)\)
a,rút gọn
b,tính F biết x=9-\(4\sqrt{5}\)
c, tìm GTNN của F
\(A=\frac{\sqrt{x}-2}{\sqrt{x}-1}vaB=\left(\frac{\sqrt{x}}{\sqrt{x}+1}+\frac{1}{\sqrt{x}-1}\right).\frac{\sqrt{x}-1}{x+1}\left(x\ge0,x\ne1\right)\)
a Tính giá trị biểu thức A khi x=9
b Rút gọn B
c Đặt P=B:(A-1)
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 \(x=4\)
Cho P= \(\left(1-\frac{\sqrt{3}}{x-9}+\frac{3}{\sqrt{x}-3}\right):\frac{\sqrt{x}}{\sqrt{x}+3}\)
a, Rút gọn biểu thức P
b, Tính giá trị P khi x=\(11+6\sqrt{2}\)
c, Tìm x để P nguyên
Rút gọn A = \(\left(\frac{3}{\sqrt{x}-1}-\frac{\sqrt{x}-3}{x-1}\right)\div\left(\frac{x+2}{x+\sqrt{x}-2}-\frac{\sqrt{x}}{\sqrt{x}+2}\right)\)
\(A=\left(\frac{3}{\sqrt{x}-1}-\frac{\sqrt{x}-3}{x-1}\right):\left(\frac{x+2}{x+\sqrt{x}-2}-\frac{\sqrt{x}}{\sqrt{x}+2}\right)\left(ĐK:x\ge0;\ne1\right)\)
\(=\left[\frac{3}{\sqrt{x}-1}-\frac{\sqrt{x}-3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\right]:\left[\frac{x+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}-\frac{\sqrt{x}}{\sqrt{x}+2}\right]\)
\(=\frac{3\left(\sqrt{x}+1\right)-\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}:\frac{x+2-\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\frac{3\sqrt{x}+3-\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}:\frac{x+2-x+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(=\frac{2\sqrt{x}+6}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{\sqrt{x}+2}\)
\(=\frac{2\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}=\frac{2\left(\sqrt{x}+3\right)}{\sqrt{x}+1}\)
giúp tớ
Cho P=\(\left(1-\frac{\sqrt{3}}{x-9}+\frac{3}{\sqrt{x}-3}\right):\frac{\sqrt{x}}{\sqrt{x}+3}\)
a, rút gọn P
b,tính giá trị P khi x=\(11+6\sqrt{2}\)
c,tìm x để P nguyên
Cho biểu thức : \(A=\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}}{1-\sqrt{xy}}+1\right):\left(1-\frac{\sqrt{xy}+\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\right)\).
a) Rút gọn A .
b) Cho \(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}=6\). Tính giá trị lớn nhất của A .
Bài 1: Rút gọn biểu thức sau
\(P=\left(\frac{1}{\sqrt{x}-\sqrt{x-1}}-\frac{x-3}{\sqrt{x-1}-\sqrt{2}}\right)\left(\frac{2}{\sqrt{2}-\sqrt{x}}-\frac{\sqrt{x}+\sqrt{2}}{\sqrt{2x}-x}\right)\)