X/(x-9)+4-(9/x-9)

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Solution for X/(x-9)+4-(9/x-9) equation: 


D( x )

x = 0

x-9 = 0

x = 0

x = 0

x-9 = 0

x-9 = 0

x-9 = 0 // + 9

x = 9

x in (-oo:0) U (0:9) U (9:+oo)

X/(x-9)-(9/x)+4+9 = 0

X/(x-9)-9*x^-1+4+9 = 0

X/(x-9)-9/x+4+9 = 0

(X*x)/(x*(x-9))+(-9*(x-9))/(x*(x-9))+(4*x*(x-9))/(x*(x-9))+(9*x*(x-9))/(x*(x-9)) = 0

4*x*(x-9)-9*(x-9)+9*x*(x-9)+X*x = 0

X*x+4*x^2+9*x^2-9*x-36*x-81*x+81 = 0

X*x+4*x^2+9*x^2-45*x-81*x+81 = 0

X*x+13*x^2-126*x+81 = 0

X*x+13*x^2-126*x+81 = 0

13*x^2-126*x+81 = 0

DELTA = (-126)^2-(4*13*81)

DELTA = 11664

DELTA > 0

x = (11664^(1/2)+126)/(2*13) or x = (126-11664^(1/2))/(2*13)

x = 9 or x = 9/13

(x-9/13)*(x-9) = 0

((x-9/13)*(x-9))/(x*(x-9)) = 0

((x-9/13)*(x-9))/(x*(x-9)) = 0 // * x*(x-9)

(x-9/13)*(x-9) = 0

( x-9/13 )

x-9/13 = 0 // + 9/13

x = 9/13

( x-9 )

x-9 = 0 // + 9

x = 9

x in { 9} 

x = 9/13

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