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

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

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

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

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

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

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

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

(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.

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

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

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

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

\(=4x+27\)

Trả lời:

( x - 3 ) ( x² + 3x + 9 ) - ( x² - 27x )

= x³ - 27 - x² + 27x

= x³ - x² + 27x - 27

  ( 3 ----- 3)-----no biết       
 

( x - 3 ) ( x² + 3x + 9 ) - x ( x² - 2 ) - 2 ( x - 1 )

= x³ - 27 - x³ + 2x - 2x + 2

= - 25

Bài 1: 

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

b: Để A=3 thì 3x-9=x+1

=>2x=10

hay x=5

Bài 2: 

a: \(A=\dfrac{x+x-2-2x-4}{\left(x-2\right)\left(x+2\right)}:\dfrac{x+2-x}{x+2}\)

\(=\dfrac{-6}{x-2}\cdot\dfrac{1}{2}=\dfrac{-3}{x-2}\)

b: Để A nguyên thì \(x-2\in\left\{1;-1;3;-3\right\}\)

hay \(x\in\left\{3;1;5;-1\right\}\)

\(B=\dfrac{x^2-x}{x^2-3x}-\dfrac{7x-9}{x^2-9}\)

\(B=\dfrac{x\left(x-1\right)}{x\left(x-3\right)}-\dfrac{7x-9}{x^2-3^2}\)

\(B=\dfrac{x-1}{x-3}-\dfrac{7x-9}{\left(x+3\right)\left(x-3\right)}\)

\(B=\dfrac{\left(x-1\right)\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}-\dfrac{7x-9}{\left(x+3\right)\left(x-3\right)}\)

\(B=\dfrac{\left(x-1\right)\left(x+3\right)-7x-9}{\left(x+3\right)\left(x-3\right)}\)

\(B=\dfrac{x^2+3x-x-3-7x+9}{\left(x+3\right)\left(x-3\right)}\)

\(B=\dfrac{x^2-5x+6}{\left(x+3\right)\left(x-3\right)}\)

\(B=\dfrac{x\left(x-5\right)+6}{\left(x+3\right)\left(x-3\right)}\)