(9/x)+(1/(x-1))=9

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Solution for (9/x)+(1/(x-1))=9 equation: 


D( x )

x = 0

x-1 = 0

x = 0

x = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:0) U (0:1) U (1:+oo)

1/(x-1)+9/x = 9 // - 9

1/(x-1)+9/x-9 = 0

(1*x)/(x*(x-1))+(9*(x-1))/(x*(x-1))+(-9*x*(x-1))/(x*(x-1)) = 0

9*(x-1)-9*x*(x-1)+1*x = 0

10*x-9*x^2+9*x-9 = 0

19*x-9*x^2-9 = 0

19*x-9*x^2-9 = 0

19*x-9*x^2-9 = 0

DELTA = 19^2-(-9*(-9)*4)

DELTA = 37

DELTA > 0

x = (37^(1/2)-19)/(-9*2) or x = (-37^(1/2)-19)/(-9*2)

x = (37^(1/2)-19)/(-18) or x = (37^(1/2)+19)/18

(x-((37^(1/2)-19)/(-18)))*(x-((37^(1/2)+19)/18)) = 0

((x-((37^(1/2)-19)/(-18)))*(x-((37^(1/2)+19)/18)))/(x*(x-1)) = 0

((x-((37^(1/2)-19)/(-18)))*(x-((37^(1/2)+19)/18)))/(x*(x-1)) = 0 // * x*(x-1)

(x-((37^(1/2)-19)/(-18)))*(x-((37^(1/2)+19)/18)) = 0

( x-((37^(1/2)+19)/18) )

x-((37^(1/2)+19)/18) = 0 // + (37^(1/2)+19)/18

x = (37^(1/2)+19)/18

( x-((37^(1/2)-19)/(-18)) )

x-((37^(1/2)-19)/(-18)) = 0 // + (37^(1/2)-19)/(-18)

x = (37^(1/2)-19)/(-18)

x in { (37^(1/2)+19)/18, (37^(1/2)-19)/(-18) }

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