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Trả lời:
( x - 3 ) ( x2 + 3x + 9 ) - ( x2 - 27x )
= x3 - 27 - x2 + 27x
= x3 - x2 + 27x - 27
(\(3+\dfrac{x}{3-x}+\dfrac{2x}{3+x}-\dfrac{4x^2-3x-9}{x^2-9}\) ):\(\left(\dfrac{2}{3-x}-\dfrac{x-1}{3x-x^2}\right)\)\(=\left(\dfrac{3x^2-27}{\left(x-3\right)\left(x+3\right)}+\dfrac{-x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\dfrac{2x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}-\dfrac{4x^2-3x-9}{\left(x-3\right)\left(x+3\right)}\right)\)\(:\left(\dfrac{2x}{x\left(3-x\right)}-\dfrac{x-1}{x\left(3-x\right)}\right)\)
\(=\dfrac{3x^2-27-x^2-3x+2x^2-6x-4x^2+3x+9}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+1}{x\left(3-x\right)}\)
\(=\dfrac{-6x-18}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+1}{x\left(3-x\right)}\) \(=\dfrac{-6\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+1}{x\left(3-x\right)}\)
\(=\dfrac{6}{3-x}.\dfrac{x\left(x-3\right)}{x+1}\) \(=\dfrac{6x}{x+1}\)
\(B=\dfrac{x^2-x}{x^2-3x}-\dfrac{7x-9}{x^2-9}\)
\(B=\dfrac{x\left(x-1\right)}{x\left(x-3\right)}-\dfrac{7x-9}{x^2-3^2}\)
\(B=\dfrac{x-1}{x-3}-\dfrac{7x-9}{\left(x+3\right)\left(x-3\right)}\)
\(B=\dfrac{\left(x-1\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}-\dfrac{7x-9}{\left(x+3\right)\left(x-3\right)}\)
\(B=\dfrac{\left(x-1\right)\left(x+3\right)-7x-9}{\left(x+3\right)\left(x-3\right)}\)
\(B=\dfrac{x^2+3x-x-3-7x+9}{\left(x+3\right)\left(x-3\right)}\)
\(B=\dfrac{x^2-5x+6}{\left(x+3\right)\left(x-3\right)}\)
\(B=\dfrac{x\left(x-5\right)+6}{\left(x+3\right)\left(x-3\right)}\)
Một lưu ý trc khi lm bài : Bn ko nên lm quá tắt tại vì biểu thức sẽ rất dễ mắc sai lầm.
\(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)\)
\(=x\left(x^2-3x+9\right)+3\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)\)
\(=x^3-3x^2+9x+3x^2-9x+27-x^3-2x^2+2x^2+4x\)
\(=\left(x^3-x^3\right)+\left(-3x^2+3x^2-2x^2+2x^2\right)+\left(9x-9x+4x\right)+27\)
\(=4x+27\)
(=) (x+3)^2. (x-3)^2.(x-3).(x+3)
(=) (x+3)^3 . (x-3)^3
dấu . là dấu nhân nhé bn