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

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


D( x )

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0

2*x-3 = 0 // + 3

2*x = 3 // : 2

x = 3/2

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

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

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

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

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

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

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

3*x-2*x^2+4*x+6*x-9-6-5 = 0

7*x-2*x^2+6*x-11-9 = 0

13*x-2*x^2-20 = 0

13*x-2*x^2-20 = 0

13*x-2*x^2-20 = 0

DELTA = 13^2-(-20*(-2)*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)-13)/(-2*2) or x = (-9^(1/2)-13)/(-2*2)

x = 5/2 or x = 4

(x-5/2)*(x-4) = 0

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

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

(x-5/2)*(x-4) = 0

( x-4 )

x-4 = 0 // + 4

x = 4

( x-5/2 )

x-5/2 = 0 // + 5/2

x = 5/2

x in { 4, 5/2 }

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