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

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Solution for (6/(x-9)(x-3))=(1/(x-9))+(3/(x-3)) equation: 


D( x )

x-3 = 0

x-9 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x-9 = 0

x-9 = 0

x-9 = 0 // + 9

x = 9

x in (-oo:3) U (3:9) U (9:+oo)

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

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

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

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

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

6*(x-3)^2-1*(x-3)-3*(x-9) = 0

6*x^2-37*x-3*x+27+57 = 0

6*x^2-40*x+84 = 0

6*x^2-40*x+84 = 0

2*(3*x^2-20*x+42) = 0

3*x^2-20*x+42 = 0

DELTA = (-20)^2-(3*4*42)

DELTA = -104

DELTA < 0

2 = 0

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

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

2 = 0

x belongs to the empty set

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