A=(\(\frac{1}{\sqrt{x}-1}\)+\(\frac{1}{\sqrt{x}+1}\))2.\(\frac{x^2-1}{2}\)-\(\sqrt{1-x^2}\)
1)tim dk cua x de bieu thuc A co nghia
2)rut gon bieu thuc A
3) giai phuong trinh theo x khi A=-2
Rut gon bieu thuc : \(\frac{2xy^2}{3ab}\sqrt{\frac{9a^3b^4}{8xy^3}}\)
rut gon bieu thuc 2x2\(\sqrt{\frac{9}{x^4}}\) voi x<0
Cho A = \(\left(\dfrac{\sqrt{x}+\sqrt{y}}{1-\sqrt{xy}}+\dfrac{\sqrt{x}-\sqrt{y}}{1+\sqrt{xy}}\right):\left(1+\dfrac{x+y+2xy}{1-xy}\right)\)
a, Rut gon bieu thuc A
b, Tinh gia tri cua A khi x = \(\dfrac{1}{1+\sqrt{2}}\)
c, Tim Max A
B=\(\left(\frac{1}{x+\sqrt{x}}+\frac{1}{\sqrt{x}+1}-1\right):\frac{\sqrt{x}-1}{\sqrt{x}-2}\)
a,Rut gon B
b,Tim cac gia tri cua x de 3B=\(2\sqrt{x}-7\)
\(\\ RUTS\:GON\:\:\:\:\:\::\:Q=\frac{1}{\sqrt{a+1}+\sqrt{a+2}}+\frac{1}{\sqrt{a+2}+\sqrt{a+3}}+....+\: \frac{1}{\sqrt{a+99}+\sqrt{a+100}}\)
\(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\)
a, rut gon A
b, tinh A voi \(4-2\sqrt{3}\)
Cho bieu thuc:\(P=\left(\frac{x+2}{\sqrt{x}+1}-\sqrt{x}\right):\left(\frac{\sqrt{x}-4}{1-x}-\frac{\sqrt{x}}{\sqrt{x}+1}\right)\)
a) Tìm ĐKXĐ và rút gọn P
b) Tìm x để P<1
c) Tìm x để P đạt giá trị nhỏ nhất
1. Rút gọn
D = \(\frac{\sqrt{1+\frac{2\sqrt{2}}{3}}+\sqrt{1-\frac{2\sqrt{2}}{3}}}{\sqrt{1+\frac{2\sqrt{2}}{3}}-\sqrt{1-\frac{2\sqrt{2}}{3}}}\)
2. Chứng minh rằng:
\(\frac{a\sqrt{b}+b}{a-b}.\sqrt{\frac{ab+b^2-2\sqrt{ab^3}}{a\left(a+2\sqrt{b}\right)+b}}\left(\sqrt{a}+\sqrt{b}\right)=b\) với ( a > b > 0 )
