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\(a,C=\dfrac{2x^2-x-x-1+2-x^2}{x-1}\left(x\ne1\right)\\ C=\dfrac{x^2-2x+1}{x-1}=\dfrac{\left(x-1\right)^2}{x-1}=x-1\\ b,D=\dfrac{1+\sqrt{a}}{\sqrt{a}\left(\sqrt{a}-1\right)}\cdot\dfrac{\left(\sqrt{a}-1\right)^2}{\sqrt{a}+1}\left(a>0;a\ne1\right)\\ D=\dfrac{\sqrt{a}-1}{\sqrt{a}}\)
Có
Câu 1:
Sửa đề: \(B=\left(\dfrac{x}{x+3\sqrt{x}}+\dfrac{1}{\sqrt{x}+3}\right):\left(1-\dfrac{2}{\sqrt{x}}+\dfrac{6}{x+3\sqrt{x}}\right)\)
Ta có: \(B=\left(\dfrac{x}{x+3\sqrt{x}}+\dfrac{1}{\sqrt{x}+3}\right):\left(1-\dfrac{2}{\sqrt{x}}+\dfrac{6}{x+3\sqrt{x}}\right)\)
\(=\left(\dfrac{x}{\sqrt{x}\left(\sqrt{x}+3\right)}+\dfrac{1}{\sqrt{x}+3}\right):\left(\dfrac{x+3\sqrt{x}-2\left(\sqrt{x}+3\right)+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\right)\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}:\dfrac{x+3\sqrt{x}-2\sqrt{x}-6+6}{\sqrt{x}\left(\sqrt{x}+3\right)}\)
\(=\dfrac{\sqrt{x}+1}{\sqrt{x}+3}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+3\right)}{x+\sqrt{x}}\)
\(=\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}=1\)
Câu 3:
Ta có: \(Q=\left(\dfrac{a}{a-2\sqrt{a}}+\dfrac{a}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}+1}{a-4\sqrt{a}+4}\)
\(=\left(\dfrac{a}{\sqrt{a}\left(\sqrt{a}-2\right)}+\dfrac{a}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}+1}{\left(\sqrt{a}-2\right)^2}\)
\(=\dfrac{a+\sqrt{a}}{\sqrt{a}-2}\cdot\dfrac{\sqrt{a}-2}{\sqrt{a}+1}\cdot\dfrac{\sqrt{a}-2}{1}\)
\(=\sqrt{a}\left(\sqrt{a}-2\right)\)
\(=a-2\sqrt{a}\)
1) \(A=3\sqrt{\dfrac{1}{3}}-\dfrac{5}{2}\sqrt{12}-\sqrt{48}\)
\(=3\cdot\dfrac{\sqrt{1}}{\sqrt{3}}-\dfrac{5\sqrt{12}}{2}-\sqrt{4^2\cdot3}\)
\(=\dfrac{3\cdot1}{\sqrt{3}}-\dfrac{5\cdot2\sqrt{3}}{2}-4\sqrt{3}\)
\(=\sqrt{3}-5\sqrt{3}-4\sqrt{3}\)
\(=-8\sqrt{3}\)
2) \(A=\sqrt{12-4x}\) có nghĩa khi:
\(12-4x\ge0\)
\(\Leftrightarrow4x\le12\)
\(\Leftrightarrow x\le\dfrac{12}{4}\)
\(\Leftrightarrow x\le3\)
3) \(\dfrac{2x-2\sqrt{x}}{x-1}\)
\(=\dfrac{2\sqrt{x}\cdot\sqrt{x}-2\sqrt{x}}{\left(\sqrt{x}\right)^2-1^2}\)
\(=\dfrac{2\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{2\sqrt{\text{x}}}{\sqrt{x}+1}\)
\(ĐK:x\ne\pm1\)
Với \(\left[{}\begin{matrix}x>1\\x< -1\end{matrix}\right.\Leftrightarrow A=\dfrac{x+2}{x^2-1}+\dfrac{x^2}{x+1}=\dfrac{x+2+x^3-x^2}{\left(x-1\right)\left(x+1\right)}\)
Với \(-1< x< 1\Leftrightarrow A=\dfrac{x+2}{1-x^2}+\dfrac{x^2}{x+1}=\dfrac{x+2+x^3-x^2}{\left(x+1\right)\left(1-x\right)}\)
\(B=2x\cdot\dfrac{2}{x}+x^2+2x+1\left(x\ne0\right)=x^2+2x+5\)
\(A=\dfrac{x+1}{2x-2}+\dfrac{x^2+3}{2-2x^2}+\dfrac{1}{1-x}-15\)
\(A=\dfrac{x+1}{2.\left(x-1\right)}+\dfrac{x^2+3}{2.\left(1-x\right).\left(1+x\right)}+\dfrac{1}{1-x}-\dfrac{15}{1}\)
\(A=\dfrac{\left(x+1\right)^2-\left(x^2+3\right)-2.\left(x+1\right)-15.2.\left(x-1\right).\left(x+1\right)}{2.\left(x-1\right).\left(x+1\right)}\)
\(A=\dfrac{x^2+2x+1-x^2-3-2x-30.\left(x^2-1\right)}{2.\left(x-1\right).\left(x+1\right)}\)
\(A=\dfrac{-4-30x^2+30}{2.\left(x-1\right).\left(x+1\right)}\)
\(A=\dfrac{26-30x^2}{2.\left(x-1\right).\left(x+1\right)}\)
\(A=\dfrac{2.\left(13-15x^2\right)}{2.\left(x-1\right).\left(x+1\right)}\)
\(A=\dfrac{13-15x^2}{\left(x-1\right).\left(x+1\right)}\)