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

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


D( x )

x = 0

(1/2)*x+1/4 = 0

x = 0

x = 0

(1/2)*x+1/4 = 0

(1/2)*x+1/4 = 0

1/2*x+1/4 = 0 // - 1/4

1/2*x = -1/4 // : 1/2

x = -1/4/1/2

x = -1/2

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

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

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

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

1/4*x-x^-1 = 0

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

1/4*x^2 = 1 // : 1/4

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+1/4) = 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 naleu017Cy do O

x in { -2, 2 }

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