((12-3x^2)/(x^2-x-6))-((3x+4)/(x-3))

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Solution for ((12-3x^2)/(x^2-x-6))-((3x+4)/(x-3)) equation: 


D( x )

x^2-x-6 = 0

x-3 = 0

x^2-x-6 = 0

x^2-x-6 = 0

x^2-x-6 = 0

DELTA = (-1)^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)+1)/(1*2) or x = (1-25^(1/2))/(1*2)

x = 3 or x = -2

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x in (-oo:-2) U (-2:3) U (3:+oo)

(12-(3*x^2))/(x^2-x-6)-((3*x+4)/(x-3)) = 0

(12-3*x^2)/(x^2-x-6)-((3*x+4)/(x-3)) = 0

(12-3*x^2)/(x^2-x-6)+(-1*(3*x+4))/(x-3) = 0

x^2-x-6 = 0

x^2-x-6 = 0

x^2-x-6 = 0

DELTA = (-1)^2-(-6*1*4)

DELTA = 25

DELTA > 0

x = (25^(1/2)+1)/(1*2) or x = (1-25^(1/2))/(1*2)

x = 3 or x = -2

(x+2)*(x-3) = 0

(12-3*x^2)/((x+2)*(x-3))+(-1*(3*x+4))/(x-3) = 0

(12-3*x^2)/((x+2)*(x-3))+(-1*(3*x+4)*(x+2))/((x+2)*(x-3)) = 0

12-1*(3*x+4)*(x+2)-3*x^2 = 0

4-6*x^2-10*x = 0

4-6*x^2-10*x = 0

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

2-3*x^2-5*x = 0

DELTA = (-5)^2-(-3*2*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+5)/(-3*2) or x = (5-49^(1/2))/(-3*2)

x = -2 or x = 1/3

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

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

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

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x-1/3 )

x-1/3 = 0 // + 1/3

x = 1/3

x in { -2} 

x = 1/3

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