3/(x+8)-9/(x-6)=-42/(x^2+2x-48)

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Solution for 3/(x+8)-9/(x-6)=-42/(x^2+2x-48) equation: 


D( x )

x-6 = 0

x^2+2*x-48 = 0

x+8 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

x^2+2*x-48 = 0

x^2+2*x-48 = 0

x^2+2*x-48 = 0

DELTA = 2^2-(-48*1*4)

DELTA = 196

DELTA > 0

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

x = 6 or x = -8

x+8 = 0

x+8 = 0

x+8 = 0 // - 8

x = -8

x in (-oo:-8) U (-8:6) U (6:+oo)

3/(x+8)-(9/(x-6)) = -42/(x^2+2*x-48) // + -42/(x^2+2*x-48)

3/(x+8)-(9/(x-6))-(-42/(x^2+2*x-48)) = 0

3/(x+8)-9*(x-6)^-1+42*(x^2+2*x-48)^-1 = 0

3/(x+8)-9/(x-6)+42/(x^2+2*x-48) = 0

x^2+2*x-48 = 0

x^2+2*x-48 = 0

x^2+2*x-48 = 0

DELTA = 2^2-(-48*1*4)

DELTA = 196

DELTA > 0

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

x = 6 or x = -8

(x+8)*(x-6) = 0

3/(x+8)-9/(x-6)+42/((x+8)*(x-6)) = 0

(3*(x-6))/((x+8)*(x-6))+(-9*(x+8))/((x+8)*(x-6))+42/((x+8)*(x-6)) = 0

3*(x-6)-9*(x+8)+42 = 0

42-6*x-90 = 0

-6*x-48 = 0

(-6*x-48)/((x+8)*(x-6)) = 0

(-6*x-48)/((x+8)*(x-6)) = 0 // * (x+8)*(x-6)

-6*x-48 = 0

-6*x-48 = 0 // + 48

-6*x = 48 // : -6

x = 48/(-6)

x = -8

x in { -8} 

x belongs to the empty set

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