(6/x)+(4/(x+1))=9

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Solution for (6/x)+(4/(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:-1) U (-1:0) U (0:+oo)

4/(x+1)+6/x = 9 // - 9

4/(x+1)+6/x-9 = 0

(4*x)/(x*(x+1))+(6*(x+1))/(x*(x+1))+(-9*x*(x+1))/(x*(x+1)) = 0

6*(x+1)-9*x*(x+1)+4*x = 0

10*x-9*x^2-9*x+6 = 0

x-9*x^2+6 = 0

x-9*x^2+6 = 0

x-9*x^2+6 = 0

DELTA = 1^2-(-9*4*6)

DELTA = 217

DELTA > 0

x = (217^(1/2)-1)/(-9*2) or x = (-217^(1/2)-1)/(-9*2)

x = (217^(1/2)-1)/(-18) or x = (217^(1/2)+1)/18

(x-((217^(1/2)-1)/(-18)))*(x-((217^(1/2)+1)/18)) = 0

((x-((217^(1/2)-1)/(-18)))*(x-((217^(1/2)+1)/18)))/(x*(x+1)) = 0

((x-((217^(1/2)-1)/(-18)))*(x-((217^(1/2)+1)/18)))/(x*(x+1)) = 0 // * x*(x+1)

(x-((217^(1/2)-1)/(-18)))*(x-((217^(1/2)+1)/18)) = 0

( x-((217^(1/2)+1)/18) )

x-((217^(1/2)+1)/18) = 0 // + (217^(1/2)+1)/18

x = (217^(1/2)+1)/18

( x-((217^(1/2)-1)/(-18)) )

x-((217^(1/2)-1)/(-18)) = 0 // + (217^(1/2)-1)/(-18)

x = (217^(1/2)-1)/(-18)

x in { (217^(1/2)+1)/18, (217^(1/2)-1)/(-18) }

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