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

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Solution for 3.5/(x-3)=(2x-1)/2 equation: 


D( x )

x-3 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

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

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

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

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

(2*3.5)/(2*(x-3))+(-1*(2*x-1)*(x-3))/(2*(x-3)) = 0

2*3.5-1*(2*x-1)*(x-3) = 0

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

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

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

DELTA = 7^2-(-2*4*4)

DELTA = 81

DELTA > 0

x = (81^(1/2)-7)/(-2*2) or x = (-81^(1/2)-7)/(-2*2)

x = -1/2 or x = 4

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

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

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

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

( x+1/2 )

x+1/2 = 0 // - 1/2

x = -1/2

( x-4 )

x-4 = 0 // + 4

x = 4

x in { -1/2, 4 }

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