6x-12y/21/x-2y/7x

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Solution for 6x-12y/21/x-2y/7x equation:


D( x )

x = 0

x = 0

x = 0

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

6*x-(((12*y)/21)/x)-(x*((2*y)/7)) = 0

6*x+(-4/7)*x^-1*y+(-2/7)*x*y = 0

6*x-4/7*x^-1*y-2/7*x*y = 0

2*x*(3-2/7*x^-2*y-1/7*y) = 0

-2/7*x^-2*y = -(3-1/7*y) // : -2/7*y

x^-2 = 7/2*y^-1*(3-1/7*y)

-2 < 0

1/(x^2) = 7/2*y^-1*(3-1/7*y) // * x^2

1 = 7/2*x^2*y^-1*(3-1/7*y) // : 7/2*y^-1*(3-1/7*y)

2/7*y*(3-1/7*y)^-1 = x^2

x^2 = 2/7*y*(3-1/7*y)^-1 // ^ 1/2

abs(x) = (2/7)^(1/2)*y^(1/2)*(3-1/7*y)^(-1/2)

x = (2/7)^(1/2)*y^(1/2)*(3-1/7*y)^(-1/2) or x = -((2/7)^(1/2)*y^(1/2)*(3-1/7*y)^(-1/2))

2*x = 0

2*x = 0 // : 2

x = 0

x in { 0}

x in { (2/7)^(1/2)*y^(1/2)*(3-1/7*y)^(-1/2), -((2/7)^(1/2)*y^(1/2)*(3-1/7*y)^(-1/2)) }

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