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

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Solution for (1/x)+(2/x+1)=(5x-1)/(x+1) 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)

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

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

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

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

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

x^2-5*x^2+2*x+2*x+x+1+2 = 0

x^2-5*x^2+4*x+x+3 = 0

5*x-4*x^2+3 = 0

5*x-4*x^2+3 = 0

5*x-4*x^2+3 = 0

DELTA = 5^2-(-4*3*4)

DELTA = 73

DELTA > 0

x = (73^(1/2)-5)/(-4*2) or x = (-73^(1/2)-5)/(-4*2)

x = (73^(1/2)-5)/(-8) or x = (73^(1/2)+5)/8

(x-((73^(1/2)-5)/(-8)))*(x-((73^(1/2)+5)/8)) = 0

((x-((73^(1/2)-5)/(-8)))*(x-((73^(1/2)+5)/8)))/(x*(x+1)) = 0

((x-((73^(1/2)-5)/(-8)))*(x-((73^(1/2)+5)/8)))/(x*(x+1)) = 0 // * x*(x+1)

(x-((73^(1/2)-5)/(-8)))*(x-((73^(1/2)+5)/8)) = 0

( x-((73^(1/2)+5)/8) )

x-((73^(1/2)+5)/8) = 0 // + (73^(1/2)+5)/8

x = (73^(1/2)+5)/8

( x-((73^(1/2)-5)/(-8)) )

x-((73^(1/2)-5)/(-8)) = 0 // + (73^(1/2)-5)/(-8)

x = (73^(1/2)-5)/(-8)

x in { (73^(1/2)+5)/8, (73^(1/2)-5)/(-8) }

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