Ta có: \(P=\left(\dfrac{2\sqrt{x}+x+1}{\sqrt{x}+1}\right)\cdot\left(1-\dfrac{x-\sqrt{x}}{\sqrt{x}-1}\right):\left(1-\sqrt{x}\right)\)
\(=\left(\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}+1}\right)\cdot\left(1-\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\right)\cdot\dfrac{1}{1-\sqrt{x}}\)
\(=\left(\sqrt{x}+1\right)\left(1-\sqrt{x}\right)\cdot\dfrac{1}{1-\sqrt{x}}\)
\(=\sqrt{x}+1\)
2. rút gọn biểu thức
P=\(\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}+1}+\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\sqrt{x}-1}\)
1) Rút gọn biểu thức
P=\(\left(\dfrac{x}{x-\sqrt{x}}+\dfrac{1}{\sqrt{x}+1}-\dfrac{2}{1-x}\right):\left(\dfrac{\sqrt{x}-2}{1-\sqrt{x}}\right)\)
1)Rút gọn biểu thức
P=\(\left(\dfrac{2\sqrt{x}-2}{x\sqrt{x}-\sqrt{x}+x-1}-\dfrac{1}{\sqrt{x}-1}\right):\left(1+\dfrac{1}{\sqrt{x}+1}\right)\)
1) Rút gọn biểu thức
P=\(\left(\dfrac{3x-6\sqrt{x}}{x\sqrt{x}-2x}-\dfrac{1}{2-\sqrt{x}}+\dfrac{\sqrt{x}-3}{\sqrt{x}}\right).\left(1-\dfrac{\sqrt{x}-3}{\sqrt{x}-2}\right)\)
1) Rút gọn biểu thức
P=\(\left(\dfrac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\dfrac{x+2\sqrt{x}+4}{x-1}\right):\left(3+\dfrac{1}{\sqrt{x}-2}+\dfrac{2}{\sqrt{x}+1}\right)\)
1) Rút gọn biểu thức
P=\(\left(\dfrac{x}{x\sqrt{x}-4\sqrt{x}}-\dfrac{6}{3\sqrt{x}-6}+\dfrac{1}{\sqrt{x}+2}\right):\left(\sqrt{x}-2+\dfrac{10-x}{\sqrt{x}+2}\right)\)
1) Rút gọn biểu thức
P=\(\left(1-\dfrac{x-3\sqrt{x}}{x-9}\right):\left(\dfrac{\sqrt{x}-3}{2-\sqrt{x}}+\dfrac{\sqrt{x}-2}{3+\sqrt{x}}-\dfrac{9-x}{x+\sqrt{x}-6}\right)\)
1) Rút gọn biểu thức
P=\(\left(\dfrac{x-2\sqrt{x}+3}{x-2\sqrt{x}-3}-\dfrac{x}{x-3\sqrt{x}}\right):\dfrac{1-\sqrt{x}}{3-\sqrt{x}}\)
Rút gọn các biểu thức sau:
a) \(\left(\dfrac{3-\sqrt{3}}{\sqrt{3}-1}+1\right)\left(\sqrt{3}-1\right)\)
b) \(\left(\dfrac{1}{\sqrt{x}+2}-\dfrac{1}{\sqrt{x}}\right)\left(\dfrac{2}{\sqrt{x+1}}\right)\) với x>0
