1/a-1/x=1/x-1/b

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Solution for 1/a-1/x=1/x-1/b equation: 


D( x )

x = 0

x = 0

x = 0

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

1/a-(1/x) = 1/x-(1/b) // - 1/x-(1/b)

1/a+1/b-(1/x)-(1/x) = 0

1/a+1/b-x^-1-x^-1 = 0

-2*x^-1 = -(a^-1+b^-1) // : -2

x^-1 = (a^-1+b^-1)/2

-1 < 0

1/(x^1) = (a^-1+b^-1)/2 // * x^1

1 = x^1*((a^-1+b^-1)/2) // : (a^-1+b^-1)/2

2*(a^-1+b^-1)^-1 = x^1

x = 2*(a^-1+b^-1)^-1

x = 2*(a^-1+b^-1)^-1

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