(3)/(x^(2)-11x+30)-(1)/(x-6)=(1)/(9x-45)

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Solution for (3)/(x^(2)-11x+30)-(1)/(x-6)=(1)/(9x-45) equation: 


D( x )

x-6 = 0

9*x-45 = 0

x^2-(11*x)+30 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

9*x-45 = 0

9*x-45 = 0

9*x-45 = 0 // + 45

9*x = 45 // : 9

x = 45/9

x = 5

x^2-(11*x)+30 = 0

x^2-(11*x)+30 = 0

x^2-11*x+30 = 0

x^2-11*x+30 = 0

DELTA = (-11)^2-(1*4*30)

DELTA = 1

DELTA > 0

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

x = 6 or x = 5

x in (-oo:5) U (5:6) U (6:+oo)

3/(x^2-(11*x)+30)-(1/(x-6)) = 1/(9*x-45) // - 1/(9*x-45)

3/(x^2-(11*x)+30)-(1/(x-6))-(1/(9*x-45)) = 0

3/(x^2-11*x+30)-(x-6)^-1-(9*x-45)^-1 = 0

3/(x^2-11*x+30)-1/(x-6)-1/(9*x-45) = 0

x^2-11*x+30 = 0

x^2-11*x+30 = 0

x^2-11*x+30 = 0

DELTA = (-11)^2-(1*4*30)

DELTA = 1

DELTA > 0

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

x = 6 or x = 5

(x-5)*(x-6) = 0

3/((x-5)*(x-6))-1/(x-6)-1/(9*x-45) = 0

(3*(9*x-45))/((x-5)*(x-6)*(9*x-45))+(-1*(x-5)*(9*x-45))/((x-5)*(x-6)*(9*x-45))+(-1*(x-5)*(x-6))/((x-5)*(x-6)*(9*x-45)) = 0

3*(9*x-45)-1*(x-5)*(9*x-45)-1*(x-5)*(x-6) = 0

117*x-9*x^2-x^2+11*x-360-30 = 0

128*x-10*x^2-390 = 0

128*x-10*x^2-390 = 0

2*(64*x-5*x^2-195) = 0

64*x-5*x^2-195 = 0

DELTA = 64^2-(-195*(-5)*4)

DELTA = 196

DELTA > 0

x = (196^(1/2)-64)/(-5*2) or x = (-196^(1/2)-64)/(-5*2)

x = 5 or x = 39/5

2*(x-5)*(x-39/5) = 0

(2*(x-5)*(x-39/5))/((x-5)*(x-6)*(9*x-45)) = 0

(2*(x-5)*(x-39/5))/((x-5)*(x-6)*(9*x-45)) = 0 // * (x-5)*(x-6)*(9*x-45)

2*(x-5)*(x-39/5) = 0

( x-39/5 )

x-39/5 = 0 // + 39/5

x = 39/5

( x-5 )

x-5 = 0 // + 5

x = 5

x in { 5} 

x = 39/5

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