1/x+1/(x+4)=1/7

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Solution for 1/x+1/(x+4)=1/7 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 = 1/7 // - 1/7

1/(x+4)+1/x-(1/7) = 0

1/(x+4)+1/x-1/7 = 0

(1*7*x)/(7*x*(x+4))+(1*7*(x+4))/(7*x*(x+4))+(-1*x*(x+4))/(7*x*(x+4)) = 0

1*7*(x+4)-1*x*(x+4)+1*7*x = 0

14*x-x^2-4*x+28 = 0

10*x-x^2+28 = 0

10*x-x^2+28 = 0

10*x-x^2+28 = 0

DELTA = 10^2-(-1*4*28)

DELTA = 212

DELTA > 0

x = (212^(1/2)-10)/(-1*2) or x = (-212^(1/2)-10)/(-1*2)

x = (2*53^(1/2)-10)/(-2) or x = (-2*53^(1/2)-10)/(-2)

(x-((2*53^(1/2)-10)/(-2)))*(x-((-2*53^(1/2)-10)/(-2))) = 0

((x-((2*53^(1/2)-10)/(-2)))*(x-((-2*53^(1/2)-10)/(-2))))/(7*x*(x+4)) = 0

((x-((2*53^(1/2)-10)/(-2)))*(x-((-2*53^(1/2)-10)/(-2))))/(7*x*(x+4)) = 0 // * 7*x*(x+4)

(x-((2*53^(1/2)-10)/(-2)))*(x-((-2*53^(1/2)-10)/(-2))) = 0

( x-((-2*53^(1/2)-10)/(-2)) )

x-((-2*53^(1/2)-10)/(-2)) = 0 // + (-2*53^(1/2)-10)/(-2)

x = (-2*53^(1/2)-10)/(-2)

( x-((2*53^(1/2)-10)/(-2)) )

x-((2*53^(1/2)-10)/(-2)) = 0 // + (2*53^(1/2)-10)/(-2)

x = (2*53^(1/2)-10)/(-2)

x in { (-2*53^(1/2)-10)/(-2), (2*53^(1/2)-10)/(-2) }

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