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

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Solution for 2(x+1)/(x^2-4x+3)+6x/(x-3)=3x/(x-1) equation: 


D( x )

x-3 = 0

x^2-(4*x)+3 = 0

x-1 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

x^2-(4*x)+3 = 0

x^2-(4*x)+3 = 0

x^2-4*x+3 = 0

x^2-4*x+3 = 0

DELTA = (-4)^2-(1*3*4)

DELTA = 4

DELTA > 0

x = (4^(1/2)+4)/(1*2) or x = (4-4^(1/2))/(1*2)

x = 3 or x = 1

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:3) U (3:+oo)

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

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

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

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

x^2-4*x+3 = 0

x^2-4*x+3 = 0

x^2-4*x+3 = 0

DELTA = (-4)^2-(1*3*4)

DELTA = 4

DELTA > 0

x = (4^(1/2)+4)/(1*2) or x = (4-4^(1/2))/(1*2)

x = 3 or x = 1

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

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

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

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

6*x^2-3*x^2-4*x+9*x+2 = 0

3*x^2+5*x+2 = 0

3*x^2+5*x+2 = 0

3*x^2+5*x+2 = 0

DELTA = 5^2-(2*3*4)

DELTA = 1

DELTA > 0

x = (1^(1/2)-5)/(2*3) or x = (-1^(1/2)-5)/(2*3)

x = -2/3 or x = -1

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

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

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

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

( x+1 )

x+1 = 0 // - 1

x = -1

( x+2/3 )

x+2/3 = 0 // - 2/3

x = -2/3

x in { -1, -2/3 }

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