x/(x-2)-1/(4-x)=2/(x-2)(x-4)

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Solution for x/(x-2)-1/(4-x)=2/(x-2)(x-4) equation: 


D( x )

x-2 = 0

4-x = 0

x-2 = 0

x-2 = 0

x-2 = 0 // + 2

x = 2

4-x = 0

4-x = 0

4-x = 0 // - 4

-x = -4 // * -1

x = 4

x in (-oo:2) U (2:4) U (4:+oo)

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

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

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

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

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

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

2*x^2-x^2+3*x-16*x+2+32 = 0

x^2-13*x+34 = 0

x^2-13*x+34 = 0

x^2-13*x+34 = 0

DELTA = (-13)^2-(1*4*34)

DELTA = 33

DELTA > 0

x = (33^(1/2)+13)/(1*2) or x = (13-33^(1/2))/(1*2)

x = (33^(1/2)+13)/2 or x = (13-33^(1/2))/2

(x-((13-33^(1/2))/2))*(x-((33^(1/2)+13)/2)) = 0

((x-((13-33^(1/2))/2))*(x-((33^(1/2)+13)/2)))/((x-2)*(4-x)) = 0

((x-((13-33^(1/2))/2))*(x-((33^(1/2)+13)/2)))/((x-2)*(4-x)) = 0 // * (x-2)*(4-x)

(x-((13-33^(1/2))/2))*(x-((33^(1/2)+13)/2)) = 0

( x-((13-33^(1/2))/2) )

x-((13-33^(1/2))/2) = 0 // + (13-33^(1/2))/2

x = (13-33^(1/2))/2

( x-((33^(1/2)+13)/2) )

x-((33^(1/2)+13)/2) = 0 // + (33^(1/2)+13)/2

x = (33^(1/2)+13)/2

x in { (13-33^(1/2))/2, (33^(1/2)+13)/2 }

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