x+(4x/2-3)=12/(x-3)

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Solution for x+(4x/2-3)=12/(x-3) 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)

x+(4*x)/2-3 = 12/(x-3) // - 12/(x-3)

x-(12/(x-3))+(4*x)/2-3 = 0

x-12*(x-3)^-1+(4*x)/2-3 = 0

x-12/(x-3)+2*x-3 = 0

(x*(x-3))/(x-3)-12/(x-3)+(2*x*(x-3))/(x-3)+(-3*(x-3))/(x-3) = 0

x*(x-3)+2*x*(x-3)-3*(x-3)-12 = 0

x^2+2*x^2-3*x-6*x-3*x-12+9 = 0

3*x^2-9*x-3*x-12+9 = 0

3*x^2-12*x-3 = 0

3*x^2-12*x-3 = 0

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

x^2-4*x-1 = 0

DELTA = (-4)^2-(-1*1*4)

DELTA = 20

DELTA > 0

x = (20^(1/2)+4)/(1*2) or x = (4-20^(1/2))/(1*2)

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

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

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

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

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

( x-((2*5^(1/2)+4)/2) )

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

x = (2*5^(1/2)+4)/2

( x-((4-2*5^(1/2))/2) )

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

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

x in { (2*5^(1/2)+4)/2, (4-2*5^(1/2))/2 }

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