Ta có:

`x = 1/2 * (sqrt((1-a)/a) - sqrt(a/(1-a)))`

`x = 1/2 * (sqrt(1-a)/sqrt(a) - sqrt(a)/sqrt(1-a))`

`x = 1/2 * ((sqrt(1-a))^2 - (sqrt(a))^2) / (sqrt(a)sqrt(1-a))`

`x = 1/2 * (1-a - a) / sqrt(a(1-a))`

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

`x^2 = ((1-2a)^2) / ((2sqrt(a(1-a)))^2)`

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

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

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

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

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

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

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

Vì `0 < a < 1` nên `a > 0` và `1-a > 0`

`=> 4a(1-a) > 0`

`=> sqrt(1 + x^2) = 1 / (2sqrt(a(1-a)))`

Suy ra:

`B = (2asqrt(1 + x^2)) / (sqrt(1 + x^2) - x)`

`B = (2a * 1/(2sqrt(a(1-a)))) / (1/(2sqrt(a(1-a))) - (1-2a)/(2sqrt(a(1-a))))`

`B = (a / sqrt(a(1-a))) / ((1 - (1-2a)) / (2sqrt(a(1-a))))`

`B = (a / sqrt(a(1-a))) / (2a / (2sqrt(a(1-a))))`

`B = (a / sqrt(a(1-a))) / (a / sqrt(a(1-a)))`

`B = 1`