r^2-r-6/r^2+r-12

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Solution for r^2-r-6/r^2+r-12 equation: 


D( r )

r^2 = 0

r^2 = 0

r^2 = 0

1*r^2 = 0 // : 1

r^2 = 0

r = 0

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

r^2-r+r-(6/(r^2))-12 = 0

r^2-r+r-6*r^-2-12 = 0

r^2-6*r^-2-12 = 0

t_1 = r^2

1*t_1^1-6*t_1^-1-12 = 0

1*t_1^1-6*t_1^-1-12*t_1^0 = 0

(1*t_1^2-12*t_1^1-6*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-12*t_1^1-6*t_1^0) = 0

t_1^1

t_1^2-12*t_1-6 = 0

t_1^2-12*t_1-6 = 0

DELTA = (-12)^2-(-6*1*4)

DELTA = 168

DELTA > 0

t_1 = (168^(1/2)+12)/(1*2) or t_1 = (12-168^(1/2))/(1*2)

t_1 = (2*42^(1/2)+12)/2 or t_1 = (12-2*42^(1/2))/2

t_1 in { (12-2*42^(1/2))/2, (2*42^(1/2)+12)/2} 

t_1 = (12-2*42^(1/2))/2

r^2-((12-2*42^(1/2))/2) = 0

1*r^2 = (12-2*42^(1/2))/2 // : 1

r^2 = (12-2*42^(1/2))/2

t_1 = (2*42^(1/2)+12)/2

r^2-((2*42^(1/2)+12)/2) = 0

1*r^2 = (2*42^(1/2)+12)/2 // : 1

r^2 = (2*42^(1/2)+12)/2

r^2 = (2*42^(1/2)+12)/2 // ^ 1/2

abs(r) = ((2*42^(1/2)+12)^(1/2))/(2^(1/2))

r = ((2*42^(1/2)+12)^(1/2))/(2^(1/2)) or r = -(((2*42^(1/2)+12)^(1/2))/(2^(1/2)))

r in { ((2*42^(1/2)+12)^(1/2))/(2^(1/2)), -(((2*42^(1/2)+12)^(1/2))/(2^(1/2))) }

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