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
cho bieu thuc p=(x+1)(x+√x)/√x-x-√x, voi x>0
a/ rut gon bieu thuc
b/ tim gia tri cua x de gia tri cua bieu thuc p bang 2
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=\(2\sqrt{x}-7\)
rut gon bieu thuc:\(\sqrt{\frac{a+\sqrt{a^2-b}}{2}}+\frac{a\sqrt{a^2-b}}{2}\)
rut gon bieu thuc 2x2\(\sqrt{\frac{9}{x^4}}\) voi x<0
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
M=\(\dfrac{x\sqrt{x}-1}{x-\sqrt{x}}-\dfrac{x\sqrt{x}+1}{x+\sqrt{x}}+\dfrac{x+1}{\sqrt{x}}\)với x>0,\(x\ne1\)
Rut gon bieu thuc M
Tìm x để M=\(\dfrac{9}{2}\)
So sanh M va 4
cho P=\(\left(\dfrac{3}{\sqrt{x}-1}+\dfrac{\sqrt{x}-3}{x-1}\right):\left(\dfrac{x+2}{x+\sqrt{x}-2}-\dfrac{\sqrt{x}}{\sqrt{x}+2}\right)\\ \)
a, rut gon
b, tim x de P=\(\sqrt{x}-1\)
Rut gon bieu thuc : \(\frac{2xy^2}{3ab}\sqrt{\frac{9a^3b^4}{8xy^3}}\)
