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

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


D( x )

x+6 = 0

2*x+12 = 0

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

2*x+12 = 0

2*x+12 = 0

2*x+12 = 0 // - 12

2*x = -12 // : 2

x = -12/2

x = -6

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

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

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

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

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

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

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

6*x^2+72*x+216 = 0

6*x^2+72*x+216 = 0

6*(x^2+12*x+36) = 0

x^2+12*x+36 = 0

DELTA = 12^2-(1*4*36)

DELTA = 0

x = -12/(1*2)

x = -6 or x = -6

6*(x+6)^2 = 0

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

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

6*(x+6)^2 = 0

x+6 = 0 // - 6

x = -6

x in { -6} 

x belongs to the empty set

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