1/(x-2)-5/(x+6)=8/(x^2+4x-12)

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Solution for 1/(x-2)-5/(x+6)=8/(x^2+4x-12) equation: 


D( x )

x^2+4*x-12 = 0

x-2 = 0

x+6 = 0

x^2+4*x-12 = 0

x^2+4*x-12 = 0

x^2+4*x-12 = 0

DELTA = 4^2-(-12*1*4)

DELTA = 64

DELTA > 0

x = (64^(1/2)-4)/(1*2) or x = (-64^(1/2)-4)/(1*2)

x = 2 or x = -6

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

x in (-oo:-6) U (-6:2) U (2:+oo)

1/(x-2)-(5/(x+6)) = 8/(x^2+4*x-12) // - 8/(x^2+4*x-12)

1/(x-2)-(5/(x+6))-(8/(x^2+4*x-12)) = 0

1/(x-2)-5*(x+6)^-1-8*(x^2+4*x-12)^-1 = 0

1/(x-2)-5/(x+6)-8/(x^2+4*x-12) = 0

x^2+4*x-12 = 0

x^2+4*x-12 = 0

x^2+4*x-12 = 0

DELTA = 4^2-(-12*1*4)

DELTA = 64

DELTA > 0

x = (64^(1/2)-4)/(1*2) or x = (-64^(1/2)-4)/(1*2)

x = 2 or x = -6

(x+6)*(x-2) = 0

1/(x-2)-5/(x+6)-8/((x+6)*(x-2)) = 0

(1*(x+6))/((x-2)*(x+6))+(-5*(x-2))/((x-2)*(x+6))-8/((x-2)*(x+6)) = 0

1*(x+6)-5*(x-2)-8 = 0

16-4*x-8 = 0

8-4*x = 0

(8-4*x)/((x-2)*(x+6)) = 0

(8-4*x)/((x-2)*(x+6)) = 0 // * (x-2)*(x+6)

8-4*x = 0

8-4*x = 0 // - 8

-4*x = -8 // : -4

x = -8/(-4)

x = 2

x in { 2} 

x belongs to the empty set

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