(x/(3x-9))-1=(1/(x-3))

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Solution for (x/(3x-9))-1=(1/(x-3)) equation:


D( x )

x-3 = 0

3*x-9 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

3*x-9 = 0

3*x-9 = 0

3*x-9 = 0 // + 9

3*x = 9 // : 3

x = 9/3

x = 3

x in (-oo:3) U (3:+oo)

x/(3*x-9)-1 = 1/(x-3) // - 1/(x-3)

x/(3*x-9)-(1/(x-3))-1 = 0

x/(3*x-9)-(x-3)^-1-1 = 0

x/(3*x-9)-1/(x-3)-1 = 0

(x*(x-3))/((3*x-9)*(x-3))+(-1*(3*x-9))/((3*x-9)*(x-3))+(-1*(3*x-9)*(x-3))/((3*x-9)*(x-3)) = 0

x*(x-3)-1*(3*x-9)-1*(3*x-9)*(x-3) = 0

x^2-3*x^2-6*x+18*x-27+9 = 0

12*x-2*x^2-18 = 0

12*x-2*x^2-18 = 0

2*(6*x-x^2-9) = 0

6*x-x^2-9 = 0

DELTA = 6^2-(-9*(-1)*4)

DELTA = 0

x = -6/(-1*2)

x = 3 or x = 3

2*(x-3)^2 = 0

(2*(x-3)^2)/((3*x-9)*(x-3)) = 0

(2*(x-3)^2)/((3*x-9)*(x-3)) = 0 // * (3*x-9)*(x-3)

2*(x-3)^2 = 0

x-3 = 0 // + 3

x = 3

x in { 3}

x belongs to the empty set

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