(x^2-x-6)/(x^2-4)=3

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


D( x )

x^2-4 = 0

x^2-4 = 0

x^2-4 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

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

(x^2-x-6)/(x^2-4) = 3 // - 3

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

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

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

6-2*x^2-x = 0

6-2*x^2-x = 0

6-2*x^2-x = 0

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

DELTA = 49

DELTA > 0

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

x = -2 or x = 3/2

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

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

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

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x-3/2 )

x-3/2 = 0 // + 3/2

x = 3/2

x in { -2} 

x = 3/2

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