6/(2x+12)+6/(x+6)+6/x=1

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Solution for 6/(2x+12)+6/(x+6)+6/x=1 equation:


D( x )

x = 0

x+6 = 0

2*x+12 = 0

x = 0

x = 0

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

2*x+12 = 0

2*x+12 = 0

2*x+12 = 0 // - 12

2*x = -12 // : 2

x = -12/2

x = -6

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

6/(2*x+12)+6/(x+6)+6/x = 1 // - 1

6/(2*x+12)+6/(x+6)+6/x-1 = 0

(6*x*(x+6))/(x*(2*x+12)*(x+6))+(6*x*(2*x+12))/(x*(2*x+12)*(x+6))+(6*(2*x+12)*(x+6))/(x*(2*x+12)*(x+6))+(-1*x*(2*x+12)*(x+6))/(x*(2*x+12)*(x+6)) = 0

6*x*(x+6)+6*x*(2*x+12)+6*(2*x+12)*(x+6)-1*x*(2*x+12)*(x+6) = 0

18*x^2-2*x^3+12*x^2-24*x^2+108*x+144*x-72*x+432 = 0

30*x^2-2*x^3-24*x^2+252*x-72*x+432 = 0

6*x^2-2*x^3+180*x+432 = 0

6*x^2-2*x^3+180*x+432 = 0

2*(3*x^2-x^3+90*x+216) = 0

3*x^2-x^3+90*x+216 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 9, -9, 12, -12, 18, -18, 24, -24, 27, -27, 36, -36, 54, -54, 72, -72, 108, -108, 216, -216 }

1

x = 1

3*x^2-x^3+90*x+216 = 308

1

-1

x = -1

3*x^2-x^3+90*x+216 = 130

-1

2

x = 2

3*x^2-x^3+90*x+216 = 400

2

-2

x = -2

3*x^2-x^3+90*x+216 = 56

-2

3

x = 3

3*x^2-x^3+90*x+216 = 486

3

-3

x = -3

3*x^2-x^3+90*x+216 = 0

-3

x+3

6*x-x^2+72

3*x^2-x^3+90*x+216

x+3

x^3+3*x^2

6*x^2+90*x+216

-6*x^2-18*x

72*x+216

-72*x-216

0

6*x-x^2+72 = 0

DELTA = 6^2-(-1*4*72)

DELTA = 324

DELTA > 0

x = (324^(1/2)-6)/(-1*2) or x = (-324^(1/2)-6)/(-1*2)

x = -6 or x = 12

x in { -6, 12, -3}

2*(x+6)*(x-12)*(x+3) = 0

(2*(x+6)*(x-12)*(x+3))/(x*(2*x+12)*(x+6)) = 0

(2*(x+6)*(x-12)*(x+3))/(x*(2*x+12)*(x+6)) = 0 // * x*(2*x+12)*(x+6)

2*(x+6)*(x-12)*(x+3) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x+6 )

x+6 = 0 // - 6

x = -6

( x-12 )

x-12 = 0 // + 12

x = 12

x in { -6}

x in { -3, 12 }

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