5/(x+1)=(2/(x-8))+(1/x)

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Solution for 5/(x+1)=(2/(x-8))+(1/x) equation: 


D( x )

x = 0

x+1 = 0

x-8 = 0

x = 0

x = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x-8 = 0

x-8 = 0

x-8 = 0 // + 8

x = 8

x in (-oo:-1) U (-1:0) U (0:8) U (8:+oo)

5/(x+1) = 2/(x-8)+1/x // - 2/(x-8)+1/x

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

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

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

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

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

3*x^2-x^2-42*x+7*x+8 = 0

2*x^2-35*x+8 = 0

2*x^2-35*x+8 = 0

2*x^2-35*x+8 = 0

DELTA = (-35)^2-(2*4*8)

DELTA = 1161

DELTA > 0

x = (1161^(1/2)+35)/(2*2) or x = (35-1161^(1/2))/(2*2)

x = (3*129^(1/2)+35)/4 or x = (35-3*129^(1/2))/4

(x-((35-3*129^(1/2))/4))*(x-((3*129^(1/2)+35)/4)) = 0

((x-((35-3*129^(1/2))/4))*(x-((3*129^(1/2)+35)/4)))/(x*(x+1)*(x-8)) = 0

((x-((35-3*129^(1/2))/4))*(x-((3*129^(1/2)+35)/4)))/(x*(x+1)*(x-8)) = 0 // * x*(x+1)*(x-8)

(x-((35-3*129^(1/2))/4))*(x-((3*129^(1/2)+35)/4)) = 0

( x-((3*129^(1/2)+35)/4) )

x-((3*129^(1/2)+35)/4) = 0 // + (3*129^(1/2)+35)/4

x = (3*129^(1/2)+35)/4

( x-((35-3*129^(1/2))/4) )

x-((35-3*129^(1/2))/4) = 0 // + (35-3*129^(1/2))/4

x = (35-3*129^(1/2))/4

x in { (3*129^(1/2)+35)/4, (35-3*129^(1/2))/4 }

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