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

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Solution for (6/(x-1))+(9/(2x-3))=3 equation: 


D( x )

2*x-3 = 0

x-1 = 0

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:3/2) U (3/2:+oo)

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

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

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

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

21*x-6*x^2+15*x-27-9 = 0

36*x-6*x^2-36 = 0

36*x-6*x^2-36 = 0

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

6*x-x^2-6 = 0

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

DELTA = 12

DELTA > 0

x = (12^(1/2)-6)/(-1*2) or x = (-12^(1/2)-6)/(-1*2)

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

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

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

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

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

( x-((-2*3^(1/2)-6)/(-2)) )

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

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

( x-((2*3^(1/2)-6)/(-2)) )

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

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

x in { (-2*3^(1/2)-6)/(-2), (2*3^(1/2)-6)/(-2) }

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