(1/x+3)-1=2x/3-x

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Solution for (1/x+3)-1=2x/3-x equation:


D( x )

x = 0

x = 0

x = 0

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

1/x-1+3 = (2*x)/3-x // - (2*x)/3-x

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

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

1/3*x^1+1*x^-1+2*x^0 = 0

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

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

x^1

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

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

DELTA = 2^2-(1*4*(1/3))

DELTA = 8/3

DELTA > 0

x = ((8/3)^(1/2)-2)/(2*(1/3)) or x = (-(8/3)^(1/2)-2)/(2*(1/3))

x = 3/2*((8/3)^(1/2)-2) or x = -3/2*((8/3)^(1/2)+2)

x in { -3/2*((8/3)^(1/2)+2), 3/2*((8/3)^(1/2)-2)}

x in { -3/2*((8/3)^(1/2)+2), 3/2*((8/3)^(1/2)-2) }

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