(x/y)-(y/x)

Solution for (x/y)-(y/x) equation:

D( x )

x = 0

x = 0

x = 0

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

x/y-(y/x) = 0

x*y^-1-(x^-1*y) = 0

t_1 = x^-1

t_1^1*(-y)+t_1^-1*y^-1 = 0

t_1^-1*y^-1-(t_1*y) = 0

t_1^-1*y^-1*(1-(t_1^2*y^2)) = 0

t_1^2*(-y^2) = -1 // : -y^2

t_1^2 = 1/(y^2)

t_1^2 = 1/(y^2) // ^ 1/2

abs(t_1) = 1/y

t_1 = 1/y or t_1 = -(1/y)

1/(t_1*y) = 0

t_1^-1*y^-1 = 0 // : y^-1

t_1^-1 = 0

t_1 należy do O

t_1 = 1/y

x^-1-(1/y) = 0

x^-1-y^-1 = 0

1*x^-1 = y^-1 // : 1

x^-1 = y^-1

-1 < 0

1/(x^1) = y^-1 // * x^1

1 = x^1*y^-1 // : y^-1

1/(y^-1) = x^1

x = 1/(y^-1)

t_1 = -(1/y)

x^-1+1/y = 0

1*x^-1 = -y^-1 // : 1

x^-1 = -y^-1

-1 < 0

1/(x^1) = -y^-1 // * x^1

1 = x^1*(-y^-1) // : -y^-1

1/(-y^-1) = x^1

x = 1/(-y^-1)

x in { 1/(y^-1), 1/(-y^-1) }