B=\(\left(\frac{\sqrt{x}}{\sqrt{x}-2}-\frac{4}{x-2\sqrt{x}}\right).\left(\frac{1}{\sqrt{x}+2}+\frac{4}{x-4}\right)\)
Rút gọn
\(\frac{1}{\sqrt{x-1}}.\sqrt{x^2-2x+1}\)
Tính:
\(A=\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+\dfrac{1}{4\sqrt{3}+3\sqrt{4}}+...+\dfrac{1}{225\sqrt{224}+224\sqrt{225}}\)
\(\frac{\sqrt{8-2\sqrt{15}}}{\sqrt{10}-\sqrt{6}}\)
Tính:
\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
Rút gọn \(A=\left(\dfrac{6x+4}{3\sqrt{3x^3}-8}-\dfrac{\sqrt{3x}}{3x+2\sqrt{3x}+4}\right).\left(\dfrac{1+3\sqrt{3x^3}}{1+\sqrt{3x}}-\sqrt{3x}\right)\)
Rút gọn:
\(A=\dfrac{3x+\sqrt{9x}-3}{x+\sqrt{x}-2}-\dfrac{\sqrt{x}+1}{\sqrt{x}+2}+\dfrac{\sqrt{x}-2}{\sqrt{x}}\cdot\left(\dfrac{1}{1-\sqrt{x}}-1\right)\)
Rút gọn : \(A=\left[\text{(\dfrac{1}{\sqrt{x}}+\dfrac{1}{\sqrt{y}}).\dfrac{2}{\sqrt{x}+\sqrt{y}}+\dfrac{1}{x}+\dfrac{1}{y}}\right]:\dfrac{\sqrt{x^3}+y\sqrt{x}+x\sqrt{y}+\sqrt{y^3}}{\sqrt{xy^3}+\sqrt{x^3y}}\)
a) Tính \(M=\sqrt{a^2+4ab^2+4b^4}-\sqrt{4a^2-12ab^2+9b^4}\)
Với \(a=\sqrt{2};b=1\)
b) Tính \(\dfrac{\sqrt{x}+\sqrt{3}}{3-x}.\left(\dfrac{x\sqrt{x}+3\sqrt{3}}{x-\sqrt{3x}+3}-2\sqrt{x}\right)\)
