(1/(n^2+10n+24))-(3n/(n^2+8n+12))

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Solution for (1/(n^2+10n+24))-(3n/(n^2+8n+12)) equation: 


D( n )

n^2+8*n+12 = 0

n^2+10*n+24 = 0

n^2+8*n+12 = 0

n^2+8*n+12 = 0

n^2+8*n+12 = 0

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

DELTA = 16

DELTA > 0

n = (16^(1/2)-8)/(1*2) or n = (-16^(1/2)-8)/(1*2)

n = -2 or n = -6

n^2+10*n+24 = 0

n^2+10*n+24 = 0

n^2+10*n+24 = 0

DELTA = 10^2-(1*4*24)

DELTA = 4

DELTA > 0

n = (4^(1/2)-10)/(1*2) or n = (-4^(1/2)-10)/(1*2)

n = -4 or n = -6

n in (-oo:-6) U (-6:-4) U (-4:-2) U (-2:+oo)

1/(n^2+10*n+24)-((3*n)/(n^2+8*n+12)) = 0

1/(n^2+10*n+24)-3*n*(n^2+8*n+12)^-1 = 0

1/(n^2+10*n+24)+(-3*n)/(n^2+8*n+12) = 0

n^2+10*n+24 = 0

n^2+10*n+24 = 0

n^2+10*n+24 = 0

DELTA = 10^2-(1*4*24)

DELTA = 4

DELTA > 0

n = (4^(1/2)-10)/(1*2) or n = (-4^(1/2)-10)/(1*2)

n = -4 or n = -6

(n+6)*(n+4) = 0

n^2+8*n+12 = 0

n^2+8*n+12 = 0

n^2+8*n+12 = 0

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

DELTA = 16

DELTA > 0

n = (16^(1/2)-8)/(1*2) or n = (-16^(1/2)-8)/(1*2)

n = -2 or n = -6

(n+6)*(n+2) = 0

1/((n+6)*(n+4))+(-3*n)/((n+6)*(n+2)) = 0

1/((n+6)*(n+4))+(-3*n*(n+4))/((n+6)*(n+4)) = 0

1-3*n*(n+4) = 0

1-3*n^2-12*n = 0

1-3*n^2-12*n = 0

1-3*n^2-12*n = 0

DELTA = (-12)^2-(-3*1*4)

DELTA = 156

DELTA > 0

n = (156^(1/2)+12)/(-3*2) or n = (12-156^(1/2))/(-3*2)

n = (2*39^(1/2)+12)/(-6) or n = (12-2*39^(1/2))/(-6)

(n-((2*39^(1/2)+12)/(-6)))*(n-((12-2*39^(1/2))/(-6))) = 0

((n-((2*39^(1/2)+12)/(-6)))*(n-((12-2*39^(1/2))/(-6))))/((n+6)*(n+4)) = 0

((n-((2*39^(1/2)+12)/(-6)))*(n-((12-2*39^(1/2))/(-6))))/((n+6)*(n+4)) = 0 // * (n+6)*(n+4)

(n-((2*39^(1/2)+12)/(-6)))*(n-((12-2*39^(1/2))/(-6))) = 0

( n-((12-2*39^(1/2))/(-6)) )

n-((12-2*39^(1/2))/(-6)) = 0 // + (12-2*39^(1/2))/(-6)

n = (12-2*39^(1/2))/(-6)

( n-((2*39^(1/2)+12)/(-6)) )

n-((2*39^(1/2)+12)/(-6)) = 0 // + (2*39^(1/2)+12)/(-6)

n = (2*39^(1/2)+12)/(-6)

n in { (12-2*39^(1/2))/(-6), (2*39^(1/2)+12)/(-6) }

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