7/(6x-2)+x/(3-x)=4

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Solution for 7/(6x-2)+x/(3-x)=4 equation: 


D( x )

6*x-2 = 0

3-x = 0

6*x-2 = 0

6*x-2 = 0

6*x-2 = 0 // + 2

6*x = 2 // : 6

x = 2/6

x = 1/3

3-x = 0

3-x = 0

3-x = 0 // - 3

-x = -3 // * -1

x = 3

x in (-oo:1/3) U (1/3:3) U (3:+oo)

7/(6*x-2)+x/(3-x) = 4 // - 4

7/(6*x-2)+x/(3-x)-4 = 0

(7*(3-x))/((6*x-2)*(3-x))+(x*(6*x-2))/((6*x-2)*(3-x))+(-4*(6*x-2)*(3-x))/((6*x-2)*(3-x)) = 0

7*(3-x)+x*(6*x-2)-4*(6*x-2)*(3-x) = 0

6*x^2+24*x^2-9*x-80*x+21+24 = 0

30*x^2-89*x+45 = 0

30*x^2-89*x+45 = 0

30*x^2-89*x+45 = 0

DELTA = (-89)^2-(4*30*45)

DELTA = 2521

DELTA > 0

x = (2521^(1/2)+89)/(2*30) or x = (89-2521^(1/2))/(2*30)

x = (2521^(1/2)+89)/60 or x = (89-2521^(1/2))/60

(x-((89-2521^(1/2))/60))*(x-((2521^(1/2)+89)/60)) = 0

((x-((89-2521^(1/2))/60))*(x-((2521^(1/2)+89)/60)))/((6*x-2)*(3-x)) = 0

((x-((89-2521^(1/2))/60))*(x-((2521^(1/2)+89)/60)))/((6*x-2)*(3-x)) = 0 // * (6*x-2)*(3-x)

(x-((89-2521^(1/2))/60))*(x-((2521^(1/2)+89)/60)) = 0

( x-((2521^(1/2)+89)/60) )

x-((2521^(1/2)+89)/60) = 0 // + (2521^(1/2)+89)/60

x = (2521^(1/2)+89)/60

( x-((89-2521^(1/2))/60) )

x-((89-2521^(1/2))/60) = 0 // + (89-2521^(1/2))/60

x = (89-2521^(1/2))/60

x in { (2521^(1/2)+89)/60, (89-2521^(1/2))/60 }

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