1/x+1/(x+4)=1/6

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Solution for 1/x+1/(x+4)=1/6 equation: 


D( x )

x+4 = 0

x = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

x = 0

x = 0

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

1/(x+4)+1/x = 1/6 // - 1/6

1/(x+4)+1/x-(1/6) = 0

1/(x+4)+1/x-1/6 = 0

(1*6*x)/(6*x*(x+4))+(1*6*(x+4))/(6*x*(x+4))+(-1*x*(x+4))/(6*x*(x+4)) = 0

1*6*(x+4)-1*x*(x+4)+1*6*x = 0

12*x-x^2-4*x+24 = 0

8*x-x^2+24 = 0

8*x-x^2+24 = 0

8*x-x^2+24 = 0

DELTA = 8^2-(-1*4*24)

DELTA = 160

DELTA > 0

x = (160^(1/2)-8)/(-1*2) or x = (-160^(1/2)-8)/(-1*2)

x = (4*10^(1/2)-8)/(-2) or x = (-4*10^(1/2)-8)/(-2)

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

((x-((4*10^(1/2)-8)/(-2)))*(x-((-4*10^(1/2)-8)/(-2))))/(6*x*(x+4)) = 0

((x-((4*10^(1/2)-8)/(-2)))*(x-((-4*10^(1/2)-8)/(-2))))/(6*x*(x+4)) = 0 // * 6*x*(x+4)

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

( x-((-4*10^(1/2)-8)/(-2)) )

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

x = (-4*10^(1/2)-8)/(-2)

( x-((4*10^(1/2)-8)/(-2)) )

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

x = (4*10^(1/2)-8)/(-2)

x in { (-4*10^(1/2)-8)/(-2), (4*10^(1/2)-8)/(-2) }

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