(1/x)+1/(x+2)=1/5

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Solution for (1/x)+1/(x+2)=1/5 equation: 


D( x )

x+2 = 0

x = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x = 0

x = 0

x in (-oo:-2) U (-2:0) U (0:+oo)

1/(x+2)+1/x = 1/5 // - 1/5

1/(x+2)+1/x-(1/5) = 0

1/(x+2)+1/x-1/5 = 0

(1*5*x)/(5*x*(x+2))+(1*5*(x+2))/(5*x*(x+2))+(-1*x*(x+2))/(5*x*(x+2)) = 0

1*5*(x+2)-1*x*(x+2)+1*5*x = 0

10*x-x^2-2*x+10 = 0

8*x-x^2+10 = 0

8*x-x^2+10 = 0

8*x-x^2+10 = 0

DELTA = 8^2-(-1*4*10)

DELTA = 104

DELTA > 0

x = (104^(1/2)-8)/(-1*2) or x = (-104^(1/2)-8)/(-1*2)

x = (2*26^(1/2)-8)/(-2) or x = (-2*26^(1/2)-8)/(-2)

(x-((2*26^(1/2)-8)/(-2)))*(x-((-2*26^(1/2)-8)/(-2))) = 0

((x-((2*26^(1/2)-8)/(-2)))*(x-((-2*26^(1/2)-8)/(-2))))/(5*x*(x+2)) = 0

((x-((2*26^(1/2)-8)/(-2)))*(x-((-2*26^(1/2)-8)/(-2))))/(5*x*(x+2)) = 0 // * 5*x*(x+2)

(x-((2*26^(1/2)-8)/(-2)))*(x-((-2*26^(1/2)-8)/(-2))) = 0

( x-((-2*26^(1/2)-8)/(-2)) )

x-((-2*26^(1/2)-8)/(-2)) = 0 // + (-2*26^(1/2)-8)/(-2)

x = (-2*26^(1/2)-8)/(-2)

( x-((2*26^(1/2)-8)/(-2)) )

x-((2*26^(1/2)-8)/(-2)) = 0 // + (2*26^(1/2)-8)/(-2)

x = (2*26^(1/2)-8)/(-2)

x in { (-2*26^(1/2)-8)/(-2), (2*26^(1/2)-8)/(-2) }

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