(-5/(3x-9))+(4/(x-3))=5/6

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Solution for (-5/(3x-9))+(4/(x-3))=5/6 equation: 


D( x )

x-3 = 0

3*x-9 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

3*x-9 = 0

3*x-9 = 0

3*x-9 = 0 // + 9

3*x = 9 // : 3

x = 9/3

x = 3

x in (-oo:3) U (3:+oo)

4/(x-3)-5/(3*x-9) = 5/6 // - 5/6

4/(x-3)-5/(3*x-9)-(5/6) = 0

4/(x-3)-5/(3*x-9)-5/6 = 0

(-5*6*(x-3))/(6*(3*x-9)*(x-3))+(4*6*(3*x-9))/(6*(3*x-9)*(x-3))+(-5*(3*x-9)*(x-3))/(6*(3*x-9)*(x-3)) = 0

4*6*(3*x-9)-5*6*(x-3)-5*(3*x-9)*(x-3) = 0

42*x-15*x^2+90*x-135-126 = 0

132*x-15*x^2-261 = 0

132*x-15*x^2-261 = 0

3*(44*x-5*x^2-87) = 0

44*x-5*x^2-87 = 0

DELTA = 44^2-(-87*(-5)*4)

DELTA = 196

DELTA > 0

x = (196^(1/2)-44)/(-5*2) or x = (-196^(1/2)-44)/(-5*2)

x = 3 or x = 29/5

3*(x-3)*(x-29/5) = 0

(3*(x-3)*(x-29/5))/(6*(3*x-9)*(x-3)) = 0

(3*(x-3)*(x-29/5))/(6*(3*x-9)*(x-3)) = 0 // * 6*(3*x-9)*(x-3)

3*(x-3)*(x-29/5) = 0

( x-29/5 )

x-29/5 = 0 // + 29/5

x = 29/5

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3} 

x = 29/5

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