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

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


D( x )

x-2 = 0

x+2 = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

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

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

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

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

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

3*x*(x-2)-1*(x-6)*(x+2)-3*(x+2)*(x-2) = 0

2*x^2-3*x^2-2*x+12+12 = 0

24-x^2-2*x = 0

24-x^2-2*x = 0

24-x^2-2*x = 0

DELTA = (-2)^2-(-1*4*24)

DELTA = 100

DELTA > 0

x = (100^(1/2)+2)/(-1*2) or x = (2-100^(1/2))/(-1*2)

x = -6 or x = 4

(x+6)*(x-4) = 0

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

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

(x+6)*(x-4) = 0

( x+6 )

x+6 = 0 // - 6

x = -6

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -6, 4 }

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