a,  \(A=\frac{x^2+3x-x+3-x^2+1}{x^2-9}\)\(.\frac{x+3}{2}\)            \(\left(x\ne3;-3\right)\)

\(A=\frac{2x+4}{\left(x-3\right)\left(x+3\right)}.\frac{x+3}{2}\)\(=\frac{2\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}.\frac{x+3}{2}\)\(=\frac{x+2}{x-3}\)

b, để \(A\in Z\Rightarrow\hept{\begin{cases}x+2⋮x-3\\x-3⋮x-3\end{cases}}\)\(\Rightarrow x+2-x+3=5⋮x-3\)\(\leftrightarrow x+3\in\left(1;5;-1;-5\right)\)

                                                                                                                              \(\leftrightarrow x\in\left(-2;2;-4;-8\right)\)

Mới 2k9

(5x - 2)(x + 1) - 3x(x² - x - 3) - 2x(x - 5)(x + 4) + 5x(x² - 7)

= 5x² + 3x - 2 - 3x³ + 3x² + 9x - 2x(x² - x - 20) + 5x³ - 35x

= 2x³ + 8x² - 23x - 2 - 2x³ + 2x² + 40x = 10x² + 17x - 2

\(B=4x\left(2x+y\right)+2y\left(2x+y-y^2+2x\right)\)

\(=4x\left(2x+y\right)+2y\left(4x-y^2+y\right)=8x^2+4xy+8xy-2y^3+2y^2\)

(-3x + 4)(x - 2) - x(x² - 2)(-4x + 1) + (2x - 5)(x² - 4x)

= -3x² + 10x - 8 - x(-4x³ + x² + 8x - 2) + 2x³ - 13x² + 20x

= 2x³ - 16x² + 30x - 8 + 4x⁴ - x³ - 8x² + 2x

= 4x⁴ + x³ - 24x² + 28x - 8

(8x - 1)(2x - 3)) - (-x + 7)(x - 2) - 6x(x² - x + 3) + (x² - 3)(x - 4)

= 16x² - 26x + 3 + x² - 9x + 14 - 6x³ + 12x² - 18x + x³ - 4x² - 3x + 12

= -5x³ + 25x² - 56x + 29

(8x - 1) (2x - 3) - (-x + 7)(x - 2) - 6x (x² - x + 3) + (x² - 3)(x - 4)

= 16x²-24x-2x-3+x²-2x-7x+14-6x³+6x-18x+x³-4x²-3x+12

=7x³+13x²-36x+23

(x - 6)(3x - 1) - 2x²(x - 2) + x(x - 1)(2x + 3) - 5x(x² - 4x + 1) 

= (3x² - 19x + 6) - (2x³ - 4x²) + (x² - x)(2x + 3) - (5x³ - 20x² + 5x) 

= 3x² - 19x + 6 - 2x³ + 4x² + 2x³ + 3x² - 2x² - 3x - 5x³ + 20x² + 5x

= -7x³ + 28x²+ 17x + 6 

-7x(2x²- 4x - 5) - (x - 5)(-2x + 3) + (3x - 2)(x+4) - 4x² (x - 3)

=-14x³+28x²+35x+2x²-3x-10x+15+3x²+12x-2x-8-4x³+12x²

=-18x³+45x²+32x+7

\(\left(3x+5\right)\left(3x-5\right)-\left(4x-3\right)^2\)

\(9x^2-25-\left(16x^2-24x+9\right)\)

\(9x^2-25-16x^2+24x-9\)

\(-7x^2+24x-34\)

(3x - 7)(x + 3) + 5x(x² - 2x - 4) - (4x - 5)(x-4)-(x + 2)(x + 1)

=3x²+9x-7x-21+5x³-10x²-20x-4x²+16x+5x-20-x²-x-2x-2

=5x³-13x²-43

5x² (x - 7) - 4x(x - 2)(x + 3) - (x - 5)(x + 6) + (2x-1)(x + 5)

=5x³-35x²-4x(x²+3x-2x-6)-(x²+6x-5x-30)+2x²+10x-x-5

=5x³-35x²-4x³-12x²+8x²+24x-x²-6x+5x+30+2x²+9x-5

=x³+32x²+32x+25