-7/(x-3)=1/(2x-6)+1

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Solution for -7/(x-3)=1/(2x-6)+1 equation: 


D( x )

x-3 = 0

2*x-6 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

2*x-6 = 0

2*x-6 = 0

2*x-6 = 0 // + 6

2*x = 6 // : 2

x = 6/2

x = 3

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

-7/(x-3) = 1/(2*x-6)+1 // - 1/(2*x-6)+1

-7/(x-3)-(1/(2*x-6))-1 = 0

-7/(x-3)-(2*x-6)^-1-1 = 0

-7/(x-3)-1/(2*x-6)-1 = 0

(-7*(2*x-6))/((x-3)*(2*x-6))+(-1*(x-3))/((x-3)*(2*x-6))+(-1*(x-3)*(2*x-6))/((x-3)*(2*x-6)) = 0

-7*(2*x-6)-1*(x-3)-1*(x-3)*(2*x-6) = 0

12*x-2*x^2-15*x-18+45 = 0

27-2*x^2-3*x = 0

27-2*x^2-3*x = 0

27-2*x^2-3*x = 0

DELTA = (-3)^2-(-2*4*27)

DELTA = 225

DELTA > 0

x = (225^(1/2)+3)/(-2*2) or x = (3-225^(1/2))/(-2*2)

x = -9/2 or x = 3

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

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

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

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

( x+9/2 )

x+9/2 = 0 // - 9/2

x = -9/2

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 3} 

x = -9/2

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