(1/x)+1/(x+4)=1/3

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Solution for (1/x)+1/(x+4)=1/3 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 = 1/3 // - 1/3

1/(x+4)+1/x-(1/3) = 0

1/(x+4)+1/x-1/3 = 0

(1*3*x)/(3*x*(x+4))+(1*3*(x+4))/(3*x*(x+4))+(-1*x*(x+4))/(3*x*(x+4)) = 0

1*3*(x+4)-1*x*(x+4)+1*3*x = 0

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

2*x-x^2+12 = 0

2*x-x^2+12 = 0

2*x-x^2+12 = 0

DELTA = 2^2-(-1*4*12)

DELTA = 52

DELTA > 0

x = (52^(1/2)-2)/(-1*2) or x = (-52^(1/2)-2)/(-1*2)

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

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

((x-((2*13^(1/2)-2)/(-2)))*(x-((-2*13^(1/2)-2)/(-2))))/(3*x*(x+4)) = 0

((x-((2*13^(1/2)-2)/(-2)))*(x-((-2*13^(1/2)-2)/(-2))))/(3*x*(x+4)) = 0 // * 3*x*(x+4)

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

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

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

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

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

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

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

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

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