giúp mình câu 1 trước đi nè

Câu 2:

a, ĐKXĐ: x\(\ge\)0; x\(\ne\)\(\pm\)1

B=

\(\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{\left(\sqrt{x}-1\right)^2-\left(\sqrt{x}-1\right)^2}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{-2.2\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{-4\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}:\dfrac{\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{4\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}.\dfrac{\sqrt{x}+1}{\sqrt{x}}\\ =-\dfrac{4}{\sqrt{x}-1}\)

1: \(=\dfrac{3x+\sqrt{x}-3\sqrt{x}-1-3\sqrt{x}+1+8\sqrt{x}}{9x-1}:\dfrac{3\sqrt{x}+1-3\sqrt{x}+2}{3\sqrt{x}+1}\)

\(=\dfrac{3x+3\sqrt{x}}{9x-1}\cdot\dfrac{3\sqrt{x}+1}{3}\)

\(=\dfrac{x+\sqrt{x}}{3\sqrt{x}-1}\)

2: Để P>=0 thì 3 căn x-1>0

hay x>1/9

Câu 1: 

a: \(P=\dfrac{x+\sqrt{x}-2}{\sqrt{x}\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)

\(=\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}\cdot\dfrac{\sqrt{x}+1}{\sqrt{x}}=\dfrac{\sqrt{x}+1}{\sqrt{x}}\)

b: Để \(2P=2\sqrt{5}+5\) thì \(P=\dfrac{2\sqrt{5}+5}{2}\) 

\(\Leftrightarrow\sqrt{x}\left(2\sqrt{5}+5\right)=2\left(\sqrt{x}+1\right)\)

\(\Leftrightarrow\sqrt{x}\left(2\sqrt{5}+3\right)=2\)

hay \(x=\dfrac{4}{29+12\sqrt{5}}=\dfrac{4\left(29-12\sqrt{5}\right)}{121}\)

Câu 1: 

a: \(P=\dfrac{x+\sqrt{x}-2}{\sqrt{x}\left(\sqrt{x}+2\right)}\cdot\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)

\(=\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}\cdot\dfrac{\sqrt{x}+1}{\sqrt{x}}=\dfrac{\sqrt{x}+1}{\sqrt{x}}\)

b: Để \(2P=2\sqrt{5}+5\) thì \(P=\dfrac{2\sqrt{5}+5}{2}\) 

\(\Leftrightarrow\sqrt{x}\left(2\sqrt{5}+5\right)=2\left(\sqrt{x}+1\right)\)

\(\Leftrightarrow\sqrt{x}\left(2\sqrt{5}+3\right)=2\)

hay \(x=\dfrac{4}{29+12\sqrt{5}}=\dfrac{4\left(29-12\sqrt{5}\right)}{121}\)​

Bài 1:

a: \(=\sqrt{7}-2+2=\sqrt{7}\)

b: \(=\left(5\sqrt{5}-3\sqrt{3}\right)\cdot\dfrac{\sqrt{5}+\sqrt{3}}{8+\sqrt{15}}\)

\(=\dfrac{\left(\sqrt{5}-\sqrt{3}\right)\cdot\left(8+\sqrt{15}\right)\cdot\left(\sqrt{5}+\sqrt{3}\right)}{8+\sqrt{15}}\)

=5-3=2

Bài 2:

a: \(A=\left(5+\sqrt{5}\right)\left(\sqrt{5}-2\right)+\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{4}-\dfrac{3\sqrt{5}\left(3-\sqrt{5}\right)}{4}\)

\(=-5+3\sqrt{5}+\dfrac{5+\sqrt{5}-9\sqrt{5}+15}{4}\)

\(=-5+3\sqrt{5}+5-2\sqrt{5}=\sqrt{5}\)

b: \(B=\left(\dfrac{x+\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}\right):\dfrac{x+3\sqrt{x}-2\left(\sqrt{x}+3\right)+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\)

\(=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{x+3\sqrt{x}+6-2\sqrt{x}-6}=1\)

a: \(=\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\dfrac{1}{2}\sqrt{2}\right)\cdot5\sqrt{6}\)

\(=\left(2\sqrt{6}-4\sqrt{3}+\dfrac{9}{2}\sqrt{2}\right)\cdot5\sqrt{6}\)

\(=60-20\sqrt{18}+\dfrac{45}{2}\sqrt{12}\)

\(=60-60\sqrt{2}+45\sqrt{3}\)

b: \(=\dfrac{\sqrt{5}+\sqrt{2}+\sqrt{5}-\sqrt{2}+3}{3}\cdot\dfrac{1}{3+2\sqrt{2}}\)

\(=\dfrac{2\sqrt{5}+3}{3}\cdot\dfrac{1}{3+2\sqrt{2}}=\dfrac{2\sqrt{5}+3}{9+6\sqrt{2}}\)

ĐKXĐ : \(x\ge0\) ; \(x\ne4\) và \(x\ne9\)

\(A=\left(\dfrac{\sqrt{x}+2}{x-5\sqrt{x}+6}-\dfrac{\sqrt{x}+3}{2-\sqrt{x}}-\dfrac{\sqrt{x}+2}{\sqrt{x}-3}\right):\left(2-\dfrac{\sqrt{x}}{\sqrt{x}+1}\right)\)

\(=\left(\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}+\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right):\left(\dfrac{2\left(\sqrt{x}+1\right)}{\sqrt{x}+1}-\dfrac{\sqrt{x}}{\sqrt{x}+1}\right)\)

\(=\dfrac{\sqrt{x}+2+x-9-x+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}:\dfrac{2\sqrt{x}+2-\sqrt{x}}{\sqrt{x}+1}\)

\(=\dfrac{\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}:\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\)

\(=\dfrac{1}{\sqrt{x}-2}.\dfrac{\sqrt{x}+1}{\sqrt{x}-2}\)

\(=\dfrac{\sqrt{x}+1}{x-4}\)

Câu b : \(\dfrac{1}{A}< \dfrac{1}{5}\Leftrightarrow\dfrac{x-4}{\sqrt{x}+1}< \dfrac{1}{5}\Leftrightarrow5x-20< \sqrt{x}+1\Leftrightarrow5x-\sqrt{x}-21< 0\)Mysterious Person Tới đây làm sao nữa :(((

\(\text{a) }ĐKXĐ:x\ge0;x\ne4;x\ne9\\ A=\left(\dfrac{\sqrt{x}+2}{x-5\sqrt{x}+6}-\dfrac{\sqrt{x}+3}{2-\sqrt{x}}-\dfrac{\sqrt{x}+2}{\sqrt{x}-3}\right):\left(2-\dfrac{\sqrt{x}}{\sqrt{x}+1}\right)\\ =\left(\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}+\dfrac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\dfrac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\right):\left(\dfrac{2\left(\sqrt{x}+1\right)}{\sqrt{x}+1}-\dfrac{\sqrt{x}}{\sqrt{x}+1}\right)\\ =\dfrac{\sqrt{x}+2+x-9-x+4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}:\dfrac{2\sqrt{x}+2-\sqrt{x}}{\sqrt{x}+1}\\ =\dfrac{\sqrt{x}-3}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}:\dfrac{\sqrt{x}+2}{\sqrt{x}+1}\\ =\dfrac{\sqrt{x}+1}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\\ =\dfrac{\sqrt{x}+1}{x-4}\)

\(b\text{) }\dfrac{1}{A}\le\dfrac{1}{5}\\ \Leftrightarrow A\ge5\\ \Leftrightarrow\dfrac{\sqrt{x}+1}{x-4}\ge5\\ \Leftrightarrow\dfrac{\sqrt{x}+1}{x-4}-5\ge0\\ \Leftrightarrow\dfrac{\sqrt{x}+1-5\left(x-4\right)}{x-4}\ge0\\ \Leftrightarrow\dfrac{\sqrt{x}+1-5x+20}{x-4}\ge0\\ \Leftrightarrow\dfrac{\sqrt{x}-5x+21}{x-4}\ge0\\ \Leftrightarrow\dfrac{\left(\sqrt{x}-\dfrac{1+\sqrt{421}}{10}\right)\left(\sqrt{x}-\dfrac{1-\sqrt{421}}{10}\right)}{\sqrt{x}-2}\ge0\)

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