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

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Solution for x/(x+1)+(x+1)/x=3 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)

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

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

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

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

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

1-x^2-x = 0

1-x^2-x = 0

1-x^2-x = 0

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

DELTA = 5

DELTA > 0

x = (5^(1/2)+1)/(-1*2) or x = (1-5^(1/2))/(-1*2)

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

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

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

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

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

( x-((1-5^(1/2))/(-2)) )

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

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

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

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

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

x in { (1-5^(1/2))/(-2), (5^(1/2)+1)/(-2) }

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