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a) \(=x^3-\dfrac{1}{27}-x^2+\dfrac{2}{3}x-\dfrac{1}{9}=x^3-x^2+\dfrac{2}{3}x-\dfrac{2}{27}\)
b) \(=x^6-6x^4+12x^2-8-x^3+x+x^2-3x=x^6-6x^4-x^3+13x^2-2x-8\)
Bạn ơi mik ra \(\dfrac{x^3+45x-54}{12\left(x-3\right)\left(x+3\right)}\) có đúng không bạn?
Mình rút chx hết bạn bạn gửi cách làm bạn qua mình tham khảo đc k ạ?
a: \(P=\left(\dfrac{3x+6}{2\left(x^2+4\right)}-\dfrac{2x^2-x-10}{\left(x+1\right)\left(x^2+1\right)}\right):\left(\dfrac{10\left(x^2-1\right)+3\left(x^2+1\right)\left(x-1\right)-6\left(x+1\right)\left(x^2+1\right)}{\left(x^2+1\right)\left(x+1\right)\left(x-1\right)\cdot2}\right)\cdot\dfrac{2}{x-1}\)
\(=\left(\dfrac{\left(3x+6\right)\left(x^3+x^2+x+1\right)-\left(2x^2+8\right)\left(2x^2-x-10\right)}{2\left(x^2+4\right)\left(x+1\right)\left(x^2+1\right)}\right)\cdot\dfrac{\left(x^2+1\right)\left(x-1\right)\left(x+1\right)\cdot2}{-3x^3+x^2-3x-13}\cdot\dfrac{2}{x-1}\)
\(=\dfrac{-x^4+11x^3+13x^2+17x+16}{\left(x^2+4\right)}\cdot\dfrac{2}{-3x^3+x^2-3x-13}\)
Ta có: \(A=\left(\dfrac{x-2}{x+2}+\dfrac{x}{x-2}+\dfrac{2x+4}{4-x^2}\right)\cdot\left(x+\dfrac{5}{x-3}\right)\)
\(=\left(\dfrac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}+\dfrac{x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\dfrac{2x+4}{\left(x-2\right)\left(x+2\right)}\right)\cdot\left(\dfrac{x\left(x-3\right)+5}{\left(x-3\right)}\right)\)
\(=\dfrac{x^2-4x+4+x^2+2x-2x-4}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x^2-3x+5}{x-3}\)
\(=\dfrac{2x^2-4x}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x^2-3x+5}{x-3}\)
\(=\dfrac{2x\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\cdot\dfrac{x^2-3x+5}{x-3}\)
\(=\dfrac{2x\left(x^2-3x+5\right)}{\left(x+2\right)\left(x-3\right)}\)
a) Ta có: \(A=\left(\dfrac{2}{x+2}-\dfrac{1}{x-3}+\dfrac{5-x}{x^2-x-6}\right)\cdot\left(x-\dfrac{6}{x-1}\right)\)
\(=\left(\dfrac{2\left(x-3\right)}{\left(x+2\right)\left(x-3\right)}-\dfrac{x+2}{\left(x-3\right)\left(x+2\right)}+\dfrac{5-x}{\left(x-3\right)\left(x+2\right)}\right)\cdot\dfrac{x\left(x-1\right)-6}{x-1}\)
\(=\dfrac{2x-6-x-2+5-x}{\left(x+2\right)\left(x-3\right)}\cdot\dfrac{x^2-x-6}{x-1}\)
\(=\dfrac{-3}{x-1}\)
\(P=\left[\dfrac{x^2}{2x-9}\left(\dfrac{3}{x}-\dfrac{1}{x-3}\right)-\dfrac{x+6}{2\left(x-3\right)}\right]:\dfrac{x+2}{2\left(x-3\right)}\)
\(\Leftrightarrow P=\left[\dfrac{x^2}{2x-9}\left(\dfrac{3\left(x-3\right)}{x\left(x-3\right)}-\dfrac{x}{x\left(x-3\right)}\right)-\dfrac{x+6}{2\left(x-3\right)}\right]:\dfrac{x+2}{2\left(x-3\right)}\)
\(\Leftrightarrow P=\left[\dfrac{x^2}{2x-9}.\dfrac{3x-9-x}{x\left(x-3\right)}-\dfrac{x+6}{2\left(x-3\right)}\right]:\dfrac{x+2}{2\left(x-3\right)}\)
\(\Leftrightarrow P=\left[\dfrac{x^2}{2x-9}.\dfrac{2x-9}{x\left(x-3\right)}-\dfrac{x+6}{2\left(x-3\right)}\right]:\dfrac{x+2}{2\left(x-3\right)}\)
\(\Leftrightarrow P=\left[\dfrac{x^2.\left(2x-9\right)}{\left(2x-9\right)x\left(x-3\right)}-\dfrac{x+6}{2\left(x-3\right)}\right]:\dfrac{x+2}{2\left(x-3\right)}\)
\(\Leftrightarrow P=\left[\dfrac{x}{x-3}-\dfrac{x+6}{2\left(x-3\right)}\right]:\dfrac{x+2}{2\left(x-3\right)}\)
\(\Leftrightarrow P=\left[\dfrac{2x}{2\left(x-3\right)}-\dfrac{x+6}{2\left(x-3\right)}\right]:\dfrac{x+2}{2\left(x-3\right)}\)
\(\Leftrightarrow P=\dfrac{2x-\left(x+6\right)}{2\left(x-3\right)}:\dfrac{x+2}{2\left(x-3\right)}\)
\(\Leftrightarrow P=\dfrac{2x-x-6}{2\left(x-3\right)}:\dfrac{x+2}{2\left(x-3\right)}\)
\(\Leftrightarrow P=\dfrac{x-6}{2\left(x-3\right)}:\dfrac{x+2}{2\left(x-3\right)}\)
\(\Leftrightarrow P=\dfrac{x-6}{2\left(x-3\right)}.\dfrac{2\left(x-3\right)}{x+2}\)
\(\Leftrightarrow P=\dfrac{\left(x-6\right).2\left(x-3\right)}{2\left(x-3\right).\left(x+2\right)}\)
\(\Leftrightarrow P=\dfrac{x-6}{x+2}\)