(18/x-1)*(x-1/8x^2-24x)/(24/x^2-9)

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Solution for (18/x-1)*(x-1/8x^2-24x)/(24/x^2-9) equation: 


D( x )

x = 0

24/(x^2)-9 = 0

x^2 = 0

x = 0

x = 0

24/(x^2)-9 = 0

24/(x^2)-9 = 0

24*x^-2 = 9 // : 24

x^-2 = 3/8

-2 < 0

1/(x^2) = 3/8 // * x^2

1 = 3/8*x^2 // : 3/8

8/3 = x^2

x^2 = 8/3 // ^ 1/2

abs(x) = (8/3)^(1/2)

x = (8/3)^(1/2) or x = -(8/3)^(1/2)

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in (-oo:-(8/3)^(1/2)) U (-(8/3)^(1/2):0) U (0:(8/3)^(1/2)) U ((8/3)^(1/2):+oo)

((18/x-1)*(x-((1/8)*x^2)-(24*x)))/(24/(x^2)-9) = 0

((18/x-1)*((-1/8)*x^2+x-24*x))/(24/(x^2)-9) = 0

((18*x^-1-1)*(-1/8*x^2-23*x))/(24*x^-2-9) = 0

-1/8*x^2-23*x = 0

-x*(1/8*x+23) = 0

1/8*x+23 = 0 // - 23

1/8*x = -23 // : 1/8

x = -23/1/8

x = -184

-x*(x+184) = 0

(-x*(18*x^-1-1)*(x+184))/(24*x^-2-9) = 0

( -x )

-1*x = 0 // : -1

x = 0

( 18*x^-1-1 )

18*x^-1 = 1 // : 18

x^-1 = 1/18

-1 < 0

1/(x^1) = 1/18 // * x^1

1 = 1/18*x^1 // : 1/18

18 = x^1

x = 18

( x+184 )

x+184 = 0 // - 184

x = -184

x in { 0} 

x in { 18, -184 }

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