`A = ( sqrtx/(sqrtx + 2) + 2/(sqrtx - 2) ) : (x + 4)/(sqrtx + 2) (x >= 0, x ne 4)`
`= ( (sqrtx(sqrtx - 2))/((sqrtx + 2)(sqrtx - 2)) + (2(sqrtx + 2))/((sqrtx - 2)(sqrtx + 2)) ) : (x + 4)/(sqrtx + 2)`
`= ( (x - 2sqrtx)/(x - 4) + (2sqrtx + 4)/(x - 4) ) : (x + 4)/(sqrtx + 2)`
`= (x - 2sqrtx + 2sqrtx + 4)/(x - 4). (sqrtx + 2)/(x + 4)`
`= (x + 4)/(x - 4). (sqrtx + 2)/(x + 4)`
`= (sqrtx + 2)/(x - 4)`
`= (sqrtx + 2)/((sqrtx - 2)(sqrtx + 2)'`
`= 1/(sqrtx - 2)`
`B = (1/(sqrtx - 2) + 1/(sqrtx + 2)) (sqrtx - 2)/(sqrtx) (x > 0, x ne 4)`
`= ( (sqrtx + 2)/((sqrtx - 2)(sqrtx + 2)) + (sqrtx - 2)/((sqrtx + 2)(sqrtx - 2)) ) (sqrtx - 2)/(sqrtx)`
`= ( (sqrtx + 2)/(x - 4) + (sqrtx - 2)/(x - 4) ) (sqrtx - 2)/(sqrtx)`
`= (2sqrtx)/(x - 4) (sqrtx - 2)/(sqrtx)`
`= 2/((sqrtx - 2)(sqrtx + 2)) (sqrtx - 2)`
`= 2/(sqrtx + 2)`
`C = (sqrta + 1)/(sqrta - 1) - (sqrta - 1)/(sqrta + 1) (a in mathbb R, a >= 0, a ne 1)`
`= (sqrta + 1)^2/((sqrta - 1)(sqrta + 1)) - (sqrta - 1)^2/((sqrta + 1)(sqrta - 1))`
`= (a + 2sqrta + 1)/(a - 1) - (a - 2sqrta + 1)/(a - 1)`
`= (a + 2sqrta + 1 - a + 2sqrta - 1)/(a - 1)`
`= (4sqrta)/(a - 1)`
`D = (1/(sqrta - 1) - 1/(sqrta + 1)) : (a + 1)/(a - 1) (a >= 0, a ne 1)`
`= ( (sqrta + 1)/((sqrta - 1)(sqrta + 1)) - (sqrta - 1)/((sqrta + 1)(sqrta - 1)) ) : (a + 1)/(a - 1)`
`= ( (sqrta + 1)/(a - 1) - (sqrta - 1)/(a - 1) ) : (a + 1)/(a - 1)`
`= (sqrta + 1 - sqrta + 1)/(a - 1). (a - 1)/(a + 1)`
`= 2/(a + 1)`
