(x-4/x)/(x/2-1)

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Solution for (x-4/x)/(x/2-1) equation: 


D( x )

x/2-1 = 0

x = 0

x/2-1 = 0

x/2-1 = 0

1/2*x-1 = 0 // + 1

1/2*x = 1 // : 1/2

x = 1/1/2

x = 2

x = 0

x = 0

x in (-oo:0) U (0:2) U (2:+oo)

(x-(4/x))/(x/2-1) = 0

(x-4*x^-1)/(x/2-1) = 0

(x-4*x^-1)/(1/2*x-1) = 0

x-4*x^-1 = 0

x^-1*(x^2-4) = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x^-1*(x-2)*(x+2) = 0

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x-2 )

x-2 = 0 // + 2

x = 2

( x^-1 )

1*x^-1 = 0 // : 1

x^-1 = 0

x należy do O

x in { 2} 

x = -2

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