(0.5x-10)/(x-4)=(0.5x+2)/(2x-8)

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Solution for (0.5x-10)/(x-4)=(0.5x+2)/(2x-8) equation:


D( x )

2*x-8 = 0

x-4 = 0

2*x-8 = 0

2*x-8 = 0

2*x-8 = 0 // + 8

2*x = 8 // : 2

x = 8/2

x = 4

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:4) U (4:+oo)

(0.5*x-10)/(x-4) = (0.5*x+2)/(2*x-8) // - (0.5*x+2)/(2*x-8)

(0.5*x-10)/(x-4)-((0.5*x+2)/(2*x-8)) = 0

(0.5*x-10)/(x-4)+(-1*(0.5*x+2))/(2*x-8) = 0

((0.5*x-10)*(2*x-8))/((x-4)*(2*x-8))+(-1*(0.5*x+2)*(x-4))/((x-4)*(2*x-8)) = 0

(0.5*x-10)*(2*x-8)-1*(0.5*x+2)*(x-4) = 0

0.5*x^2-24*x+88 = 0

0.5*x^2-24*x+88 = 0

0.5*x^2-24*x+88 = 0

DELTA = (-24)^2-(0.5*4*88)

DELTA = 400

DELTA > 0

x = (400^(1/2)+24)/(0.5*2) or x = (24-400^(1/2))/(0.5*2)

x = 44 or x = 4

(x-4)*(x-44) = 0

((x-4)*(x-44))/((x-4)*(2*x-8)) = 0

((x-4)*(x-44))/((x-4)*(2*x-8)) = 0 // * (x-4)*(2*x-8)

(x-4)*(x-44) = 0

( x-4 )

x-4 = 0 // + 4

x = 4

( x-44 )

x-44 = 0 // + 44

x = 44

x in { 4}

x = 44

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