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

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Solution for (8/(x-1))-(9/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:0) U (0:1) U (1:+oo)

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

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

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

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

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

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

x-x^2-x+9 = 0

9-x^2 = 0

(9-x^2)/(x*(x-1)) = 0

(9-x^2)/(x*(x-1)) = 0 // * x*(x-1)

9-x^2 = 0

-1*x^2 = -9 // : -1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x in { 3, -3 }

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