1+(7/x)=6/x^2

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Solution for 1+(7/x)=6/x^2 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

7/x+1 = 6/(x^2) // - 6/(x^2)

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

7/x-6*x^-2+1 = 0

7*x^-1-6*x^-2+1 = 0

t_1 = x^-1

7*t_1^1-6*t_1^2+1 = 0

7*t_1-6*t_1^2+1 = 0

DELTA = 7^2-(-6*1*4)

DELTA = 73

DELTA > 0

t_1 = (73^(1/2)-7)/(-6*2) or t_1 = (-73^(1/2)-7)/(-6*2)

t_1 = (73^(1/2)-7)/(-12) or t_1 = (73^(1/2)+7)/12

t_1 = (73^(1/2)-7)/(-12)

x^-1-((73^(1/2)-7)/(-12)) = 0

1*x^-1 = (73^(1/2)-7)/(-12) // : 1

x^-1 = (73^(1/2)-7)/(-12)

-1 < 0

1/(x^1) = (73^(1/2)-7)/(-12) // * x^1

1 = ((73^(1/2)-7)/(-12))*x^1 // : (73^(1/2)-7)/(-12)

-12*(73^(1/2)-7)^-1 = x^1

x = -12*(73^(1/2)-7)^-1

t_1 = (73^(1/2)+7)/12

x^-1-((73^(1/2)+7)/12) = 0

1*x^-1 = (73^(1/2)+7)/12 // : 1

x^-1 = (73^(1/2)+7)/12

-1 < 0

1/(x^1) = (73^(1/2)+7)/12 // * x^1

1 = ((73^(1/2)+7)/12)*x^1 // : (73^(1/2)+7)/12

12*(73^(1/2)+7)^-1 = x^1

x = 12*(73^(1/2)+7)^-1

x in { -12*(73^(1/2)-7)^-1, 12*(73^(1/2)+7)^-1 }

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