1/(3x-6)-5/(x-2)=12

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Solution for 1/(3x-6)-5/(x-2)=12 equation: 


D( x )

x-2 = 0

3*x-6 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

3*x-6 = 0

3*x-6 = 0

3*x-6 = 0 // + 6

3*x = 6 // : 3

x = 6/3

x = 2

x in (-oo:2) U (2:+oo)

1/(3*x-6)-(5/(x-2)) = 12 // - 12

1/(3*x-6)-(5/(x-2))-12 = 0

1/(3*x-6)-5*(x-2)^-1-12 = 0

1/(3*x-6)-5/(x-2)-12 = 0

(1*(x-2))/((3*x-6)*(x-2))+(-5*(3*x-6))/((3*x-6)*(x-2))+(-12*(3*x-6)*(x-2))/((3*x-6)*(x-2)) = 0

1*(x-2)-5*(3*x-6)-12*(3*x-6)*(x-2) = 0

144*x-36*x^2-14*x-144+28 = 0

130*x-36*x^2-116 = 0

130*x-36*x^2-116 = 0

2*(65*x-18*x^2-58) = 0

65*x-18*x^2-58 = 0

DELTA = 65^2-(-58*(-18)*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)-65)/(-18*2) or x = (-49^(1/2)-65)/(-18*2)

x = 29/18 or x = 2

2*(x-29/18)*(x-2) = 0

(2*(x-29/18)*(x-2))/((3*x-6)*(x-2)) = 0

(2*(x-29/18)*(x-2))/((3*x-6)*(x-2)) = 0 // * (3*x-6)*(x-2)

2*(x-29/18)*(x-2) = 0

( x-2 )

x-2 = 0 // + 2

x = 2

( x-29/18 )

x-29/18 = 0 // + 29/18

x = 29/18

x in { 2} 

x = 29/18

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