1/(x-3)-4/(x+6)=9/(x^2+3x-18)

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Solution for 1/(x-3)-4/(x+6)=9/(x^2+3x-18) equation: 


D( x )

x^2+3*x-18 = 0

x-3 = 0

x+6 = 0

x^2+3*x-18 = 0

x^2+3*x-18 = 0

x^2+3*x-18 = 0

DELTA = 3^2-(-18*1*4)

DELTA = 81

DELTA > 0

x = (81^(1/2)-3)/(1*2) or x = (-81^(1/2)-3)/(1*2)

x = 3 or x = -6

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

x in (-oo:-6) U (-6:3) U (3:+oo)

1/(x-3)-(4/(x+6)) = 9/(x^2+3*x-18) // - 9/(x^2+3*x-18)

1/(x-3)-(4/(x+6))-(9/(x^2+3*x-18)) = 0

1/(x-3)-4*(x+6)^-1-9*(x^2+3*x-18)^-1 = 0

1/(x-3)-4/(x+6)-9/(x^2+3*x-18) = 0

x^2+3*x-18 = 0

x^2+3*x-18 = 0

x^2+3*x-18 = 0

DELTA = 3^2-(-18*1*4)

DELTA = 81

DELTA > 0

x = (81^(1/2)-3)/(1*2) or x = (-81^(1/2)-3)/(1*2)

x = 3 or x = -6

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

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

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

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

18-3*x-9 = 0

9-3*x = 0

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

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

9-3*x = 0

9-3*x = 0 // - 9

-3*x = -9 // : -3

x = -9/(-3)

x = 3

x in { 3} 

x belongs to the empty set

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