(b/x)-(x/a)=x/b

Solution for (b/x)-(x/a)=x/b equation:

D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

b/x-(x/a) = x/b // - x/b

b/x-(x/a)-(x/b) = 0

b*x^-1-(a^-1*x)-(b^-1*x) = 0

x*(b*x^-2-a^-1-b^-1) = 0

b*x^-2 = -(-a^-1-b^-1) // : b

x^-2 = (a^-1+b^-1)/b

-2 < 0

1/(x^2) = (a^-1+b^-1)/b // * x^2

1 = x^2*((a^-1+b^-1)/b) // : (a^-1+b^-1)/b

1/((a^-1+b^-1)/b) = x^2

x^2 = 1/((a^-1+b^-1)/b) // ^ 1/2

abs(x) = 1/(((a^-1+b^-1)^(1/2))/(b^(1/2)))

x = 1/(((a^-1+b^-1)^(1/2))/(b^(1/2))) or x = -(1/(((a^-1+b^-1)^(1/2))/(b^(1/2))))

x = 0

x = 0

x in { 0} 

x in { 1/(((a^-1+b^-1)^(1/2))/(b^(1/2))), -(1/(((a^-1+b^-1)^(1/2))/(b^(1/2)))) }