Câu c mình làm rồi: Mn ơi, hướng dẫn em cách để giống mẫu đi ạ! - Hoc24

\(d,\dfrac{x}{x^3-27}=\dfrac{x}{\left(x-3\right)\left(x^2+3x+9\right)}=\dfrac{x\left(x-3\right)}{\left(x-3\right)^2\left(x^2+3x+9\right)}\\ \dfrac{x+2}{x^2-6x+9}=\dfrac{x+2}{\left(x-3\right)^2}=\dfrac{\left(x+2\right)\left(x^2+3x+9\right)}{\left(x-3\right)^2\left(x^2+3x+9\right)}\\ \dfrac{x-1}{x^2+3x+9}=\dfrac{\left(x-1\right)\left(x-3\right)^2}{\left(x-3\right)^2\left(x^2+3x+9\right)}\)

\(f,\dfrac{x+2}{x^2-3x+2}=\dfrac{x+2}{\left(x-1\right)\left(x-2\right)}=\dfrac{\left(x+2\right)\left(2x-3\right)}{\left(x-1\right)\left(x-2\right)\left(2x-3\right)}\\ \dfrac{x}{-2x^2+5x-3}=\dfrac{-x}{\left(2x-3\right)\left(x-1\right)}=\dfrac{-x\left(x-2\right)}{\left(2x-3\right)\left(x-1\right)\left(x-2\right)}\\ \dfrac{2x+1}{-2x^2+7x-6}=\dfrac{-\left(2x+1\right)}{\left(x-2\right)\left(2x-3\right)}=\dfrac{-\left(2x+1\right)\left(x-1\right)}{\left(x-1\right)\left(x-2\right)\left(2x-3\right)}\)

\(\dfrac{a+x}{6x^2-ax-2a^2}=\dfrac{\left(a+x\right)}{\left(2x+a\right)\left(3x-2a\right)}\)

\(\dfrac{a-x}{3x^2+4ax-4a^2}=\dfrac{a-x}{\left(x+2a\right)\left(3x-2a\right)}\)

Do đó ta quy đồng:

\(\dfrac{a+x}{6x^2-ax-2a^2}=\dfrac{\left(a+x\right)\left(x+2a\right)}{\left(x+2a\right)\left(2x+a\right)\left(3x-2a\right)}\)

\(\dfrac{a-x}{3x^2+4ax-4a^2}=\dfrac{\left(a-x\right)\left(2x+a\right)}{\left(x+2a\right)\left(2x+a\right)\left(3x-2a\right)}\)

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Hok tốt !!!!!!!!!

những từ láy cùng nghĩ với từ thút thít là : nức nở, sụt sùi, sụt sịt, ti tí, rưng rức, hu hu, ...

   nhớ k cho mk nha

b, \(cos^25x-sin^2x=0\)

\(\Leftrightarrow cos^25x-cos^2\left(x-\dfrac{\pi}{2}\right)=0\)

\(\Leftrightarrow\left[cos5x-cos\left(x-\dfrac{\pi}{2}\right)\right]\left[cos5x+cos\left(x-\dfrac{\pi}{2}\right)\right]=0\)

\(\Leftrightarrow-4sin\left(3x-\dfrac{\pi}{4}\right).sin\left(2x+\dfrac{\pi}{4}\right).cos\left(3x-\dfrac{\pi}{4}\right).cos\left(2x+\dfrac{\pi}{4}\right)=0\)

\(\Leftrightarrow-sin\left(6x-\dfrac{\pi}{2}\right).sin\left(4x+\dfrac{\pi}{2}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sin\left(6x-\dfrac{\pi}{2}\right)=0\\sin\left(4x+\dfrac{\pi}{2}\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}6x-\dfrac{\pi}{2}=k\pi\\4x+\dfrac{\pi}{2}=k\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{12}+\dfrac{k\pi}{6}\\x=-\dfrac{\pi}{8}+\dfrac{k\pi}{4}\end{matrix}\right.\)

a, \(\left(cos5x-2\right)\left(3cosx+2\right)=0\)

\(\Leftrightarrow3cosx+2=0\)

\(\Leftrightarrow cosx=-\dfrac{2}{3}\)

\(\Leftrightarrow x=\pm arccos\left(-\dfrac{2}{3}\right)+k2\pi\)

a) Ta có: \(\left(3x+1\right)^3\)

\(=\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot1+3\cdot3x\cdot1^2+1^3\)

\(=27x^3+27x^2+9x+1\)

b) Ta có: \(\left(2x-\dfrac{1}{x}\right)^3\)

\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot\dfrac{1}{x}+3\cdot2x\cdot\left(\dfrac{1}{x}\right)^2-\left(\dfrac{1}{x}\right)^3\)

\(=8x^3-12x+\dfrac{6}{x}-\dfrac{1}{x^3}\)