(=) (x+3)^2. (x-3)^2.(x-3).(x+3)

(=) (x+3)^3 . (x-3)^3 

dấu . là dấu  nhân nhé bn 

(\(3+\dfrac{x}{3-x}+\dfrac{2x}{3+x}-\dfrac{4x^2-3x-9}{x^2-9}\) ):\(\left(\dfrac{2}{3-x}-\dfrac{x-1}{3x-x^2}\right)\)\(=\left(\dfrac{3x^2-27}{\left(x-3\right)\left(x+3\right)}+\dfrac{-x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}+\dfrac{2x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}-\dfrac{4x^2-3x-9}{\left(x-3\right)\left(x+3\right)}\right)\)\(:\left(\dfrac{2x}{x\left(3-x\right)}-\dfrac{x-1}{x\left(3-x\right)}\right)\)

\(=\dfrac{3x^2-27-x^2-3x+2x^2-6x-4x^2+3x+9}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+1}{x\left(3-x\right)}\) 

\(=\dfrac{-6x-18}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+1}{x\left(3-x\right)}\) \(=\dfrac{-6\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}:\dfrac{x+1}{x\left(3-x\right)}\) 

\(=\dfrac{6}{3-x}.\dfrac{x\left(x-3\right)}{x+1}\) \(=\dfrac{6x}{x+1}\)

(x+3)(x²-3x+9)-x(x-2)(x+2)=x³+27-x(x²-4)

=x³+27-x³+4x

=4x+27

Một lưu ý trc khi lm bài : Bn ko nên lm quá tắt tại vì biểu thức sẽ rất dễ mắc sai lầm.

\(\left(x+3\right)\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)\)

\(=x\left(x^2-3x+9\right)+3\left(x^2-3x+9\right)-x\left(x-2\right)\left(x+2\right)\)

\(=x^3-3x^2+9x+3x^2-9x+27-x^3-2x^2+2x^2+4x\)

\(=\left(x^3-x^3\right)+\left(-3x^2+3x^2-2x^2+2x^2\right)+\left(9x-9x+4x\right)+27\)

\(=4x+27\)

a: ĐKXĐ: x∉{3;-3;2}

\(P=\left(\frac{x^2-3x}{x^2-9}-1\right):\left(\frac{9-x^2}{x^2+x-6}-\frac{x-3}{2-x}-\frac{x-2}{x+3}\right)\)

\(=\left(\frac{x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}-1\right):\left(\frac{\left(3-x\right)\left(3+x\right)}{\left(x+3\right)\left(x-2\right)}+\frac{x-3}{x-2}-\frac{x-2}{x+3}\right)\)

\(=\left(\frac{x}{x+3}-1\right):\left(\frac{3-x}{x-2}+\frac{x-3}{x-2}-\frac{x-2}{x+3}\right)=\frac{x-x-3}{x+3}:\frac{-\left(x-2\right)}{x+3}=\frac{-3}{-\left(x-2\right)}=\frac{3}{x-2}\)

b: \(x^3-4x=0\)

=>x*(x-2)(x+2)=0

=>x∈{0;2;-2}

mà x∉{3;-3;2}

nên x=0 hoặc x=-2

Khi x=0 thì \(P=\frac{3}{x-2}=\frac{3}{0-2}=-\frac32\)

Khi x=-2 thì \(P=\frac{3}{x-2}=\frac{3}{-2-2}=-\frac34\)

\(A=\left(\dfrac{3x-x^2}{9-x^2}-1\right):\left(\dfrac{9-x^2}{x^2+x-6}+\dfrac{x-3}{2-x}-\dfrac{x+2}{x+3}\right)\left(dk:x\ne\pm3,x\ne2\right)\)

\(=\dfrac{3x-x^2-9+x^2}{9-x^2}:\left(\dfrac{9-x^2}{\left(x-2\right)\left(x+3\right)}-\dfrac{x-3}{x-2}-\dfrac{x+2}{x+3}\right)\)

\(=\dfrac{3x-9}{9-x^2}:\dfrac{9-x^2-\left(x-3\right)\left(x+3\right)-\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x+3\right)}\)

\(=-\dfrac{3\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}.\dfrac{\left(x-2\right)\left(x+3\right)}{9-x^2-\left(x^2-9\right)-\left(x^2-4\right)}\)

\(=-\dfrac{3}{x+3}.\dfrac{\left(x-2\right)\left(x+3\right)}{9-x^2-x^2+9-x^2+4}\)

\(=\dfrac{-3\left(x-2\right)}{22-3x^2}\)

\(=\dfrac{-3x+6}{22-3x^2}\)

Vậy \(A=\dfrac{-3x+6}{22-3x^2}\) với \(x\ne\pm3,x\ne2\)