(9/x)=(8/(x+1))+(1/(x-1))

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Solution for (9/x)=(8/(x+1))+(1/(x-1)) equation: 


D( x )

x = 0

x+1 = 0

x-1 = 0

x = 0

x = 0

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

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

9/x = 8/(x+1)+1/(x-1) // - 8/(x+1)+1/(x-1)

9/x-(8/(x+1))-(1/(x-1)) = 0

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

9/x-8/(x+1)-1/(x-1) = 0

(-8*x*(x-1))/(x*(x+1)*(x-1))+(-1*x*(x+1))/(x*(x+1)*(x-1))+(9*(x+1)*(x-1))/(x*(x+1)*(x-1)) = 0

9*(x+1)*(x-1)-8*x*(x-1)-1*x*(x+1) = 0

9*x^2-9*x^2+7*x-9 = 0

7*x-9 = 0

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

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

7*x-9 = 0

7*x-9 = 0 // + 9

7*x = 9 // : 7

x = 9/7

x = 9/7

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