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d: \(\left(\dfrac{1}{2}x-1\right)\left(2x-3\right)\)
\(=x^2-\dfrac{3}{2}x-2x+3\)
\(=x^2-\dfrac{7}{2}x+3\)
e: Ta có: \(\left(x-7\right)\left(x-5\right)\)
\(=x^2-5x-7x+35\)
\(=x^2-12x+35\)
f: Ta có: \(\left(x-\dfrac{1}{2}\right)\left(x+\dfrac{1}{2}\right)\left(4x-1\right)\)
\(=4\left(x-\dfrac{1}{4}\right)\left(x-\dfrac{1}{4}\right)\)
\(=4\left(x-\dfrac{1}{4}\right)^2\)
\(=4\left(x^2-\dfrac{1}{2}x+\dfrac{1}{16}\right)\)
\(=4x^2-2x+\dfrac{1}{4}\)
Bài 1:
1: \(\dfrac{3}{5}\cdot\dfrac{2}{5}\cdot\dfrac{-3}{4}=-\dfrac{9}{50}\)
2: \(1\dfrac{1}{17}\cdot1\dfrac{1}{24}\cdot\left(-5.1\right)=\dfrac{18}{17}\cdot\dfrac{25}{24}\cdot\dfrac{-51}{10}=\dfrac{-45}{8}\)
\(P=\dfrac{\sqrt{x}+5\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}-2\right)}:\dfrac{x-4-x}{\sqrt{x}\left(\sqrt{x}-2\right)}=\dfrac{6\sqrt{x}-4}{-4}=\dfrac{2-3\sqrt{x}}{2}\)
\(P=\left(\dfrac{1}{\sqrt{x}-2}+\dfrac{5\sqrt{x}-4}{x-2\sqrt{x}}\right):\left(\dfrac{2+\sqrt{x}}{\sqrt{x}}-\dfrac{\sqrt{x}}{\sqrt{x}-2}\right)\)
\(=\dfrac{2\left(3\sqrt{x}-2\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}:\dfrac{x-4-x}{\left(\sqrt{x}-2\right)\cdot\sqrt{x}}\)
\(=\dfrac{-3\sqrt{x}+2}{2}\)
A