3x+2/(2x-1)=x-12/(x+6)

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Solution for 3x+2/(2x-1)=x-12/(x+6) equation: 


D( x )

2*x-1 = 0

x+6 = 0

2*x-1 = 0

2*x-1 = 0

2*x-1 = 0 // + 1

2*x = 1 // : 2

x = 1/2

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

x in (-oo:-6) U (-6:1/2) U (1/2:+oo)

2/(2*x-1)+3*x = x-(12/(x+6)) // - x-(12/(x+6))

2/(2*x-1)+12/(x+6)+3*x-x = 0

(2*(x+6))/((2*x-1)*(x+6))+(12*(2*x-1))/((2*x-1)*(x+6))+(3*x*(2*x-1)*(x+6))/((2*x-1)*(x+6))+(-x*(2*x-1)*(x+6))/((2*x-1)*(x+6)) = 0

2*(x+6)+12*(2*x-1)+3*x*(2*x-1)*(x+6)-x*(2*x-1)*(x+6) = 0

6*x^3-2*x^3+33*x^2-11*x^2+26*x-18*x+6*x = 0

6*x^3-2*x^3+33*x^2-11*x^2+8*x+6*x = 0

4*x^3+22*x^2+14*x = 0

4*x^3+22*x^2+14*x = 0

2*x*(2*x^2+11*x+7) = 0

2*x^2+11*x+7 = 0

DELTA = 11^2-(2*4*7)

DELTA = 65

DELTA > 0

x = (65^(1/2)-11)/(2*2) or x = (-65^(1/2)-11)/(2*2)

x = (65^(1/2)-11)/4 or x = (-(65^(1/2)+11))/4

2*x*(x+(65^(1/2)+11)/4)*(x-((65^(1/2)-11)/4)) = 0

(2*x*(x+(65^(1/2)+11)/4)*(x-((65^(1/2)-11)/4)))/((2*x-1)*(x+6)) = 0

(2*x*(x+(65^(1/2)+11)/4)*(x-((65^(1/2)-11)/4)))/((2*x-1)*(x+6)) = 0 // * (2*x-1)*(x+6)

2*x*(x+(65^(1/2)+11)/4)*(x-((65^(1/2)-11)/4)) = 0

( 2*x )

2*x = 0 // : 2

x = 0

( x+(65^(1/2)+11)/4 )

x+(65^(1/2)+11)/4 = 0 // - (65^(1/2)+11)/4

x = -((65^(1/2)+11)/4)

( x-((65^(1/2)-11)/4) )

x-((65^(1/2)-11)/4) = 0 // + (65^(1/2)-11)/4

x = (65^(1/2)-11)/4

x in { 0, -((65^(1/2)+11)/4), (65^(1/2)-11)/4 }

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