`bb 7.`

`1) A= ( (x - 2)/(x^2 - 1) - (x + 2)/(x^2 + 2x +1 ) ) . ((1 - x^2)/2)^2 (x ne +-1)`

`= (((x-2)(x+1))/((x - 1)(x + 1)(x + 1)) - ((x + 2)(x - 1))/((x - 1)(x + 1)^2 ) . ((- (x^2 - 1))/2)^2`

`= ((x^2  +x - 2x - 2)/((x - 1)(x+ 1)^2) - (x^2 - x + 2x - 2)/((x-1)(x + 1)^2) ) . ((- (x - 1)(x + 1))/2)^2`

`= ( (x^2 + x - 2x - 2 - x^2 + x - 2x + 2)/((x -1)(x + 1)^2)) . ((x-1)^2(x+1)^2)/2^2`

`= (-2x)/((x - 1)(x + 1)^2) . ((x-1)^2(x+1)^2)/4`

`= (-x (x - 1))/2`

`2) (A - 4)/5 = x`

`( (-x (x-1))/2 - 4)/5 = x`

`( (-x^2 + x - 8)/2)/10 = x`

`-x^2 + x - 8 = 10x`

`-x^2 + x - 8-10x = 0`

`-x^2 - 9x - 8 =0`

`- (x^2 + 9x + 8) = 0`

`- 1(x^2 + 8x + x + 8) = 0`

`(x^2 + 8x) + (x +8 ) =0`

`x(x+ 8) + (x + 8) =0`

`(x + 1)(x + 8) = 0`

`x = -1 (ktm)` hoặc `x = -8(tm)`

Vậy `x = -8`

`3)` 

`A = (-x (x - 1))/2`

`= (-x^2 + x)/2`

`= (-(x^2 - x + 1/4 - 1/4))/2`

`= (- (x - 1/2)^2 - 1/4))/2`

Ta có:

`(x - 1/2)^2 >= 0 AA x`

Nên `- (x - 1/2)^2 <= 0 AA x`

Suy ra: `- (x- 1/2)^2 - 1/4 <= 1/4 AA x`

Do đó: `(- (x - 1/2)^2 - 1/4))/2 <= (1/4)/2 = 1/8 < 1/2`

Vậy `A < 1/2 AA x`