(r^2-8r-12)/(r^4-6r^3)

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Solution for (r^2-8r-12)/(r^4-6r^3) equation:


D( r )

r^4-(6*r^3) = 0

r^4-(6*r^3) = 0

r^4-(6*r^3) = 0

r^4-6*r^3 = 0

r^4-6*r^3 = 0

r^3*(r-6) = 0

r-6 = 0 // + 6

r = 6

r^3 = 0

1*r^3 = 0 // : 1

r^3 = 0

r = 0

r in (-oo:0) U (0:6) U (6:+oo)

(r^2-(8*r)-12)/(r^4-(6*r^3)) = 0

(r^2-8*r-12)/(r^4-6*r^3) = 0

r^2-8*r-12 = 0

r^2-8*r-12 = 0

DELTA = (-8)^2-(-12*1*4)

DELTA = 112

DELTA > 0

r = (112^(1/2)+8)/(1*2) or r = (8-112^(1/2))/(1*2)

r = (4*7^(1/2)+8)/2 or r = (8-4*7^(1/2))/2

(r-((8-4*7^(1/2))/2))*(r-((4*7^(1/2)+8)/2)) = 0

r^4-6*r^3 = 0

r^3*(r-6) = 0

r-6 = 0 // + 6

r = 6

r^3*(r-6) = 0

((r-((8-4*7^(1/2))/2))*(r-((4*7^(1/2)+8)/2)))/(r^3*(r-6)) = 0

( r-((4*7^(1/2)+8)/2) )

r-((4*7^(1/2)+8)/2) = 0 // + (4*7^(1/2)+8)/2

r = (4*7^(1/2)+8)/2

( r-((8-4*7^(1/2))/2) )

r-((8-4*7^(1/2))/2) = 0 // + (8-4*7^(1/2))/2

r = (8-4*7^(1/2))/2

r in { (4*7^(1/2)+8)/2, (8-4*7^(1/2))/2 }

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