\(C=\dfrac{\sqrt{\dfrac{4x^2+4x+1}{x}}}{\sqrt{x}\cdot\left|2x^2-x-1\right|}=\dfrac{\left|2x+1\right|}{\sqrt{x}}\cdot\dfrac{1}{\sqrt{x}\cdot\left|\left(x-1\right)\left(2x+1\right)\right|}\)
\(=\dfrac{1}{x\left|x-1\right|}\)
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=\(\sqrt{x}-1\)
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
Bai tap: Cho:
\(A=\left(\dfrac{1}{x+\sqrt{x}}+\dfrac{1}{\sqrt{x}+1}\right):\dfrac{\sqrt{x}-1}{x+2\sqrt{x}+1}+1\)
a) Rut gon
b) Tinh gia tri cua A voi \(x=1\dfrac{1}{3}\)
RUT GON:
\(\sqrt{2x+1-2\sqrt{\left(x-1\right)\left(x+2\right)}}\)
cho x=\(\dfrac{1}{2}\)\(\sqrt{\dfrac{\sqrt{2-1}}{\sqrt{2+1}}}\)
tính f(x)= (\(4x^5+4x^4-x^3+1\))19+\(\sqrt{\left(4x^5+4x^4-5x^3+5x+3\right)^3}\)+\(\left(\dfrac{1-\sqrt{2}}{\sqrt{2x^2}+2x}\right)^{2018}\)
\(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}+1}{x+\sqrt{x}+1}-\dfrac{1}{\sqrt{x}-1}\)
a, rut gon A
b, tinh A voi \(4-2\sqrt{3}\)
Tìm x, bt :
a, \(\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}}\right):\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}-\dfrac{\sqrt{x}+2}{\sqrt{x}-1}\right)>0\)
b, \(\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{3}{x\sqrt{x}+1}+\dfrac{3}{x-\sqrt{x}+1}\right)>1\)rút gọn
A=\(\left(\dfrac{x-\sqrt{x}+2}{x-\sqrt{x}-2}-\dfrac{x}{x-2\sqrt{x}}\right)\div\dfrac{1-\sqrt{x}}{2-\sqrt{x}}\)
B=\(\left(\dfrac{1}{2\sqrt{x}+1}+\dfrac{1}{2\sqrt{x}-1}\right)\div\dfrac{1}{1-4x}\)
Rút gọn
A=\(\left(\dfrac{\sqrt{x}}{3+\sqrt{x}}+\dfrac{2x}{9-x}\right)\div\left(\dfrac{\sqrt{x}+1}{x-3\sqrt{x}}-\dfrac{2}{\sqrt{x}}\right)\)
B=\(\left(\dfrac{1}{x+\sqrt{x}}-\dfrac{1}{\sqrt{x}+1}\right)\div\dfrac{\sqrt{x}-1}{x+2\sqrt{x}+1}+1\)
