`1)`
`P = (1/(x-2) - (x^2)/(8-x^3) . (x^2 + 2x + 4)/(x+2) ) : 1/(x^2-4) (x \ne +-2)`
` = ( 1/(x-2) + (x^2)/(x^3-8) . (x^2 + 2x+4)/(x+2)) . (x^2-4)`
` = ( 1/(x-2) + (x^2)/((x-2)(x^2+2x+4)) . (x^2+2x+4)/(x+2) ) . (x^2 - 4)`
` = (1/(x-2) + (x^2)/((x-2)(x+2)) ) . (x^2 -4)`
` = ( (x+2)/(x^2 - 4) + (x^2)/(x^2-4)) . (x^2 - 4)`
` = (x + 2 + x^2)/(x^2 - 4) . (x^2 - 4)`
` = x^2 + x + 2`
Vậy `P = x^2 + x + 2` với `x \ne +-2`
`2)`
`Q = 5/(x+3) - 2/(3-x) - (3x^2 - 2x-9)/(x^2-9) ( x \ne +-3)`
` = (5 (x-3))/(x^2 - 9) + (2 (x+3))/(x^2-9) - (3x^2 - 2x-9)/(x^2-9)`
` = (5 (x-3) + 2(x+3) - (3x^2 - 2x-9))/(x^2 - 9)`
` = (5x - 15 + 2x + 6 - 3x^2 + 2x + 9)/(x^2 -9)`
` = (-3x^2 + 9x)/((x-3)(x+3))`
` = ( -3x (x-3))/((x-3)(x+3))`
` = (-3x)/(x+3)`
Vậy `Q = (-3x)/(x+3)` với `x \ne +-3`
`3)`
`A = ( (x^3+1)/(x^2-1) - (x^2-1)/(x-1) ) : (x + x/(x-1)) (x \ne +-1)`
` = ( (x^3+1)/(x^2 -1) - ( (x^2-1)(x+1))/(x^2 - 1)) : ( (x(x-1))/(x-1) + x/(x-1))`
` = (x^3 + 1 - (x^2 - 1)(x+1))/(x^2 -1) : ( x(x-1)+x)/(x-1)`
` = (x^3 + 1 - x^3 - x^2 + x + 1)/(x^2-1) : (x^2 - x + x)/(x-1)`
` = (-x^2 + x + 2)/((x-1)(x+1)) . (x-1)/(x^2)`
` = ( -x^2 + 2x - x +2)/((x-1)(x+1)) . (x-1)/(x^2)`
` = ( - x (x-2) - (x-2))/((x-1)(x+1)) . (x-1)/(x^2)`
` = ( (-x-1)(x-2))/((x-1)(x+1)) . (x-1)/(x^2)`
` = (- (x+1)(x-2))/((x-1)(x+1)). (x-1)/(x^2)`
`= ( -(x-2))/(x^2)`
`= (2-x)/(x^2)`
Vậy `A = (2-x)/(x^2)` với `x \ne +-1`
