x/x-2-3/x-1=3/(x-2)(x-1)

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


D( x )

x-2 = 0

x = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x = 0

x = 0

x in (-oo:0) U (0:2) U (2:+oo)

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

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

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

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

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

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

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

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

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

4*x-5*x^2+6 = 0

4*x-5*x^2+6 = 0

4*x-5*x^2+6 = 0

DELTA = 4^2-(-5*4*6)

DELTA = 136

DELTA > 0

x = (136^(1/2)-4)/(-5*2) or x = (-136^(1/2)-4)/(-5*2)

x = (2*34^(1/2)-4)/(-10) or x = (-2*34^(1/2)-4)/(-10)

(x-((2*34^(1/2)-4)/(-10)))*(x-((-2*34^(1/2)-4)/(-10))) = 0

((x-((2*34^(1/2)-4)/(-10)))*(x-((-2*34^(1/2)-4)/(-10))))/(x*(x-2)) = 0

((x-((2*34^(1/2)-4)/(-10)))*(x-((-2*34^(1/2)-4)/(-10))))/(x*(x-2)) = 0 // * x*(x-2)

(x-((2*34^(1/2)-4)/(-10)))*(x-((-2*34^(1/2)-4)/(-10))) = 0

( x-((-2*34^(1/2)-4)/(-10)) )

x-((-2*34^(1/2)-4)/(-10)) = 0 // + (-2*34^(1/2)-4)/(-10)

x = (-2*34^(1/2)-4)/(-10)

( x-((2*34^(1/2)-4)/(-10)) )

x-((2*34^(1/2)-4)/(-10)) = 0 // + (2*34^(1/2)-4)/(-10)

x = (2*34^(1/2)-4)/(-10)

x in { (-2*34^(1/2)-4)/(-10), (2*34^(1/2)-4)/(-10) }

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