(1/12)+(1/x)=(1/14)+(1/(x-4))

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Solution for (1/12)+(1/x)=(1/14)+(1/(x-4)) equation:


D( x )

x = 0

x-4 = 0

x = 0

x = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:0) U (0:4) U (4:+oo)

1/x+1/12 = 1/(x-4)+1/14 // - 1/(x-4)+1/14

1/x-(1/(x-4))+1/12-(1/14) = 0

1/x-(x-4)^-1+1/12-1/14 = 0

1/x-1/(x-4)+1/12-1/14 = 0

(-1*12*14*x)/(12*14*x*(x-4))+(1*12*14*(x-4))/(12*14*x*(x-4))+(1*14*x*(x-4))/(12*14*x*(x-4))+(-1*12*x*(x-4))/(12*14*x*(x-4)) = 0

1*12*14*(x-4)+1*14*x*(x-4)-1*12*x*(x-4)-1*12*14*x = 0

14*x^2-12*x^2-56*x+48*x-672 = 0

2*x^2-8*x-672 = 0

2*x^2-8*x-672 = 0

2*(x^2-4*x-336) = 0

x^2-4*x-336 = 0

DELTA = (-4)^2-(-336*1*4)

DELTA = 1360

DELTA > 0

x = (1360^(1/2)+4)/(1*2) or x = (4-1360^(1/2))/(1*2)

x = (4*85^(1/2)+4)/2 or x = (4-4*85^(1/2))/2

2*(x-((4-4*85^(1/2))/2))*(x-((4*85^(1/2)+4)/2)) = 0

(2*(x-((4-4*85^(1/2))/2))*(x-((4*85^(1/2)+4)/2)))/(12*14*x*(x-4)) = 0

(2*(x-((4-4*85^(1/2))/2))*(x-((4*85^(1/2)+4)/2)))/(12*14*x*(x-4)) = 0 // * 12*14*x*(x-4)

2*(x-((4-4*85^(1/2))/2))*(x-((4*85^(1/2)+4)/2)) = 0

( x-((4*85^(1/2)+4)/2) )

x-((4*85^(1/2)+4)/2) = 0 // + (4*85^(1/2)+4)/2

x = (4*85^(1/2)+4)/2

( x-((4-4*85^(1/2))/2) )

x-((4-4*85^(1/2))/2) = 0 // + (4-4*85^(1/2))/2

x = (4-4*85^(1/2))/2

x in { (4*85^(1/2)+4)/2, (4-4*85^(1/2))/2 }

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