\(=\dfrac{x\sqrt{x}+2x-\left(x-1\right)\left(\sqrt{x}-2\right)-\sqrt{x}-6}{x-4}:\dfrac{\sqrt{x}+2-\sqrt{x}+2}{\sqrt{x}-2}\)
\(=\dfrac{x\sqrt{x}+2x-x\sqrt{x}+2x+\sqrt{x}-2-\sqrt{x}-6}{x-4}\cdot\dfrac{\sqrt{x}-2}{4}\)
\(=\dfrac{4x-8}{x-4}\cdot\dfrac{\sqrt{x}-2}{4}=\dfrac{x-2}{\sqrt{x}+2}\)
1,\(\sqrt{x-5}+\sqrt{x+4}=3\)
2,\(\sqrt{x+4-4\sqrt{x}}+\sqrt{x+6-6\sqrt{x}}=1\)
3,\(\sqrt{x+3}-\sqrt{x-4}=1\)
4,\(\sqrt{15-x}+\sqrt{3-x}=6\)
5,\(\sqrt{10-x}+\sqrt{x+3}=5\)
6,\(\sqrt{2x-1}+\sqrt{x-2}=\sqrt{x+1}\)
7,\(\sqrt{x+6-4\sqrt{x+2}}+\sqrt{x+11-6\sqrt{x+2}}=1\)
8,\(\sqrt{x^2-5x+6}+\sqrt{x-2-3\sqrt{x-3}}=3\)
9,\(2x^2-x+4=2\sqrt{2x+3}\)
Rút gọn biểu thức
\(\frac{\left(\sqrt{x-4\sqrt{x-4}}+\sqrt{x+4\sqrt{x-4}}\right)\left(\sqrt{x-1}-1\right)}{\sqrt{x-2\sqrt{x-1}}}\)
b,\(\sqrt{x-2\sqrt{x-1}+\sqrt{x+2\sqrt{x-1}}}1\le x\le2\)
c, \(\sqrt{x+6\sqrt{x-9}}+\sqrt{x-6\sqrt{x-9}}x>18\)
d, \(\frac{1}{2\left(1+\sqrt{x+2}\right)}+\frac{1}{2\left(1-2\sqrt{x+2}\right)}\)
e,\(\frac{1}{\sqrt{x+2\sqrt{x-1}}}-\frac{1}{\sqrt{x-2\sqrt{x-1}}}\)
\(a,x^2-4x-6=\sqrt{2x^2-8x+12}\)
\(b,\sqrt{x^2+2-4\sqrt{x-2}}+\sqrt{x+7-6\sqrt{x-2}}=1\)
\(c,\sqrt{x+3+4\sqrt{x-1}}+\sqrt{8-6\sqrt{x-1}+x}=1\)
\(d,\sqrt{3-x+x^2}-\sqrt{2+x-x^2}=1\)
\(e,\sqrt{4x-9}+2\sqrt{3x^2-5x+2}=\sqrt{3x-2}+\sqrt{x-1}\)
\(\dfrac{6}{2-\sqrt{10}}-\dfrac{2\sqrt{5}-5\sqrt{2}}{\sqrt{2}-\sqrt{5}}+\sqrt{49+4\sqrt{10}}\)
\(\left(\dfrac{x-\sqrt{x}}{\sqrt{x}-1}-\dfrac{\sqrt{x}+1}{x+\sqrt{x}}\right):\dfrac{\sqrt{x}+1}{x}\)
Thu gọn P
\(P=\dfrac{x-\sqrt{x}}{x-9}+\dfrac{1}{\sqrt{x}+3}-\dfrac{1}{\sqrt{x}-3}\)
a) Tính P biết \(x=\sqrt{6+4\sqrt{2}}+\sqrt{6-4\sqrt{2}}\)
b) Tính P biết \(x=\dfrac{1}{\sqrt{2}-1}-\dfrac{1}{\sqrt{2}+1}\)
1. \(\sqrt{x-2\sqrt{x-1}}+\sqrt{x+3-4\sqrt{x-1}}\left(2< x< 5\right)\)
2. \(\frac{6}{1-\sqrt{3}}-\frac{3\sqrt{3}-1}{\sqrt{3}+1}+\sqrt{3}\)
3. \(\sqrt{29-12\sqrt{5}+\sqrt{24-8\sqrt{3}}}\)
4. \(\sqrt{\frac{4}{9-4\sqrt{5}}}-\sqrt{\frac{4}{9+4\sqrt{5}}}\)
5. \(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{x}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\)
6. \(\frac{6-\sqrt{6}}{\sqrt{6}-1}-9\sqrt{\frac{2}{3}}-\frac{4}{2-\sqrt{6}}\)
7. \(\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right)\frac{\left(\sqrt{x}-1\right)^2}{2}\left(x\ge0,x\ne1\right)\)
Giải phương trình:
\(a)\sqrt{x^2+2x+4}\ge x-2\\ b)x=\sqrt{x-\frac{1}{x}}+\sqrt{x+\frac{1}{x}}\\ c)\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2\sqrt{2x-5}}\\ d)x+y+z+4=2\sqrt{x-2}+4\sqrt{y-3}+6\sqrt{z-5}\\ e)\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\frac{1}{2}\left(x+y+z\right)\)
a : \(\dfrac{x}{x-4}+\dfrac{1}{\sqrt{x}-2}+\dfrac{1}{\sqrt{x}+2}\)với a ≥ 0 x ≠ 4
b : \(\left(\dfrac{1}{\sqrt{x}}+\dfrac{\sqrt{x}}{\sqrt{x}+1}\right).\dfrac{\sqrt{x}}{x+\sqrt{x}}\)
c : \(\dfrac{\sqrt{x}}{\sqrt{x}-1}+\dfrac{3}{\sqrt{x}+1}-\dfrac{6\sqrt{x}-4}{x-1}\)
d : \(\left[\dfrac{a+3\sqrt{a}+2}{\left(\sqrt{a}+2\right)\left(\sqrt{a}-1\right)}-\dfrac{a\sqrt{a}}{a-1}\right]:\left(\dfrac{1}{\sqrt{a}-1}+\dfrac{1}{\sqrt{a}+1}\right)\)
Tìm `ĐKXĐ`:
\(\sqrt{\dfrac{-5}{6+x}}\)
\(\sqrt{\dfrac{-2}{6-x}}\)
\(\sqrt{\dfrac{-x+3}{-6}}\)
\(\sqrt{\dfrac{7x-1}{-9}}\)
\(\sqrt{\dfrac{x+2}{x^2+2x+1}}\)
\(\sqrt{\dfrac{x-2}{x^2-2x+4}}\)
