3/(2x-5)-1/(x-2)=1

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Solution for 3/(2x-5)-1/(x-2)=1 equation: 


D( x )

2*x-5 = 0

x-2 = 0

2*x-5 = 0

2*x-5 = 0

2*x-5 = 0 // + 5

2*x = 5 // : 2

x = 5/2

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

x in (-oo:2) U (2:5/2) U (5/2:+oo)

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

3/(2*x-5)-(1/(x-2))-1 = 0

3/(2*x-5)-(x-2)^-1-1 = 0

3/(2*x-5)-1/(x-2)-1 = 0

(3*(x-2))/((2*x-5)*(x-2))+(-1*(2*x-5))/((2*x-5)*(x-2))+(-1*(2*x-5)*(x-2))/((2*x-5)*(x-2)) = 0

3*(x-2)-1*(2*x-5)-1*(2*x-5)*(x-2) = 0

x-2*x^2+9*x-10-1 = 0

10*x-2*x^2-11 = 0

10*x-2*x^2-11 = 0

10*x-2*x^2-11 = 0

DELTA = 10^2-(-11*(-2)*4)

DELTA = 12

DELTA > 0

x = (12^(1/2)-10)/(-2*2) or x = (-12^(1/2)-10)/(-2*2)

x = (2*3^(1/2)-10)/(-4) or x = (-2*3^(1/2)-10)/(-4)

(x-((2*3^(1/2)-10)/(-4)))*(x-((-2*3^(1/2)-10)/(-4))) = 0

((x-((2*3^(1/2)-10)/(-4)))*(x-((-2*3^(1/2)-10)/(-4))))/((2*x-5)*(x-2)) = 0

((x-((2*3^(1/2)-10)/(-4)))*(x-((-2*3^(1/2)-10)/(-4))))/((2*x-5)*(x-2)) = 0 // * (2*x-5)*(x-2)

(x-((2*3^(1/2)-10)/(-4)))*(x-((-2*3^(1/2)-10)/(-4))) = 0

( x-((-2*3^(1/2)-10)/(-4)) )

x-((-2*3^(1/2)-10)/(-4)) = 0 // + (-2*3^(1/2)-10)/(-4)

x = (-2*3^(1/2)-10)/(-4)

( x-((2*3^(1/2)-10)/(-4)) )

x-((2*3^(1/2)-10)/(-4)) = 0 // + (2*3^(1/2)-10)/(-4)

x = (2*3^(1/2)-10)/(-4)

x in { (-2*3^(1/2)-10)/(-4), (2*3^(1/2)-10)/(-4) }

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